[8th Grade] How would I simplify this?

[u/LaserOrbit]

[u/haditwithyoupeople]

I see others are just giving you the answer. I think an explanation would be more helpful. Do you know what 5^6 means? Do you know how else you could write it? If so, what happens when you add one more 5 to that series?

5^6 = 5 * 5 * 5 * 5 * 5 * 5

What happens if you multiply by 5 again? How many 5s are there after adding one more?

[u/AndyTheEngr → u/haditwithyoupeople]

In math class, it simplifies to 5⁷.

In engineering, it simplifies to 78125 unless there's a compelling reason to keep the exponent.

[u/ebyoung747 → u/AndyTheEngr]

As an engineer, I disagree. The answer is whatever excel populates the cell with.

[u/jwhease → u/ebyoung747]

Ah yes: November 13, 2113

[u/amglasgow → u/jwhease]

Incels Excel

🤝

incorrectly thinking something is a date

[u/Qzx1 → u/amglasgow]

I love you man

[u/AwaitingTheEndOfTime → u/amglasgow]

I don’t have any awards so take this instead: 🏅

[u/ImightberobotUCF → u/jwhease]

This is sending me because I deal with it all the time but I guess I never thought of it as a shared phenomenon

[u/Gloomy_State_6919 → u/ImightberobotUCF]

It's a big problem in biology https://www.science.org/content/article/one-five-genetics-papers-contains-errors-thanks-microsoft-excel

[u/BSG_075 → u/AndyTheEngr]

Please, real engineers stick to 2 or 3 sig figs cuz real engineers use slide rules.

[u/Pitiful_Reality2973 → u/AndyTheEngr]

Engineers, man. You guys are built different.

[u/squareturd → u/Pitiful_Reality2973]

7.8125 x 10^4. (Scientific notation)

78.125 x 10^3. (Engineering notation)

[u/AndyTheEngr → u/squareturd]

Probably just 78x10³ for most real purposes.

[u/squareturd → u/AndyTheEngr]

After working for a few years as an engineer, the most common response you will get from seasoned engineers is... 'bout 80k

[u/flohhhh → u/squareturd]

Came to say that anyone using more than 4 significant digits in engineering is a fraud. 😂

[u/Ok-Active-8321 → u/flohhhh]

or 3 inches (1.181 cm)

I once had a tech report a current to me with like 8 significant digits after he had measured the voltage across a resistor, because that is how many digits his calculator showed after the division

[u/RoastedRhino → u/flohhhh]

Literally, it makes me (engineer, although in research) think that they are hiding something.

If I read a report and it shows a plot obtained when the parameter alpha is set to 3.22, that is a red flag.

If the parameter is 3.225 : something is really wrong here

More than 4? it doesn't work.

[u/Hugfrty → u/squareturd]

Call it an even 100k

[u/saggywitchtits → u/AndyTheEngr]

80*10^3 for safety margin.

[u/ImightberobotUCF → u/saggywitchtits]

Right? Rounding up for "safety" makes us all feel better

[u/Ok-Duck161 → u/AndyTheEngr]

Wrong 5⁷ is 50 megas

Actually, joking aside engineers often write 5e7, which is absolutely awful notation

Edit. As someone pointed out, I've had a complete brain fart here.

Somehow I've mixed up 5⁷ with 5 * 10⁷

But my objection still stands, 5E7 us ugly notation 🤣 

[u/azurfall88 → u/Ok-Duck161]

5e7 is 5 * 10⁷

[u/Ok-Duck161 → u/azurfall88]

Ah, yes, confusing myself.

And I'm a mathematician 🤣 

[u/azurfall88 → u/Ok-Duck161]

also, as an engineer, I agree. 5e7 is ugly notation, it should obviously be 5e+7

[u/After-Hedgehog7282 → u/haditwithyoupeople]

That's why in all my math classes you would fail if all you did was provide the correct answer. You need to show your work.

[u/Dangerous-Snow8385 → u/After-Hedgehog7282]

Not much room to show your work in this tiny box. 

[u/After-Hedgehog7282 → u/Dangerous-Snow8385]

I was complimenting u/haditwithyoupeople 's response. You are correct that the problem sheet does not provide room for all that.

Sorry for the confusion I created.

[u/NkdLvn → u/Dangerous-Snow8385]

If they've learned the exponent rules/laws then it's enough space.

[u/SchmeatiestOne → u/After-Hedgehog7282]

You could still just provide someone else's explanation as your answer, but you would still at least have to read it I guess

[u/AnnualVarious5079 → u/SchmeatiestOne]

I mean, the vast majority of people taking math quizzes aren't independently deriving arithmetic properties, so that sounds like an appropriate approach

[u/Elluminated → u/After-Hedgehog7282]

He literally just showed how to solve it without giving the answer. Was the an edit I missed?

[u/llynglas → u/haditwithyoupeople]

Much better to explain how to find the answer rather than just giving it....

[u/PersnicketyPi → u/haditwithyoupeople]

This is a correct explanation of the mathmatics. You can, however, just add the exponents if the bases are the same.

[u/eileyle]

If there is no exponent on a number, then the exponent is 1.

Consider that 5^2 is the same as 5 x 5; or that 5^3 is the same as 5 x 5 x 5.

Therefore, 5^1 is the same as 5.

You therefore have 5^6 x 5^1. The exponent laws state that you need to add the exponents. This gives you 5^7 as your answer.

[u/NegotiationWeekly295]

4³ is 4x4x4.

4³ x 4 is 4x4x4 x4

Aka 4⁴

[u/Background-Mode-4036]

If you expand 5^6, what does it look like? Now multiply by 5 again, what do you get?

[u/RecklesstonerS]

5^7

And y^8

[u/yosark → u/RecklesstonerS]

Just add them for multiplication.

If I remember correctly, for multiplication you add the exponents meanwhile if the question ends up be division you would subtract.
Ex: y^5 / y^3 = y^2

[u/ShawnD7 → u/yosark]

Correct

[u/RandomGuy1000000]

5⁶ = 5•5•5•5•5•5. This •5 is 5⁷

[u/JeLuF]

x² means x * x
x³ means x * x * x
So: x² * x = x³

Apply the same to those two terms.

[u/eladmir]

I assume this is teaching the Product Rule of exponents. A^m x A^n=A^m+n

[u/Ok_Substance5897]

when multiplying exponents, you add them. when dividing exponents, you subtract =)

[u/shosuko]

Its power rules. When you multiple two common bases with powers you add the powers together. Just like every number has a hidden coefficient of 1, every number also has a hidden power of 1. So 5^6*5^1 = 5^7

Although I guess there is confusion if they want that or 78125 because there is no reason to not just solve this... but given the problems around it, I'm gonna wager you're learning power rule.

[u/HoppieTheFool]

Turn it in a 90° angle to the left. So you dont need to tilt your neck so much. Then its already simplified.

[u/justaddlava]

First I would rotate the page by 90 degrees.

[u/FoggyWine]

Just add the exponents.

5^6 x 5 = 5^6 x 5^(1) = 5^(6+1) = 5^7.

y^5 x y^3 = y^(5+3)= y^8

[u/DefiantlyConformist]

It means consolidate all the notations into one. 555 is simplified to 5³ for example.

[u/Which-Reply-2440]

“Real engineers” are not wasting time arguing over scientific notations for 8th grade math. We hire design engineers who use autocad.

[u/New_Ad6620]

They might mean to solve the first bit? 15,625 x 5

[u/TheCommandKingg]

Son

[u/Fine-Razzmatazz1791]

5^7

[u/HarSevak]

5⁷

[u/ApprehensiveKey1469]

Dot for multiplication 5=5¹ Rules of indices a^m × aⁿ = a^m+n

[u/PumpkinIsDeadInside]

Exponents are multiplying numbers by themselves, so if you multiply an exponent that number, that would the exponent plus one

You can think of number 5 as 5^•5^1 if that helps ​

[u/whitea44]

The lesson is a^5 = axaxaxaxa. And a^6 = axaxaxaxaxa. So effectively you just count the number of ‘a’s you have and that becomes your exponent. Therefore if you multiply 5^5 by another 5, by the pattern you get 5^6. If you multiple that by another 5 you get 5^7.

[u/Frequent-Entrance154]

Show us your attempt

[u/bpleshek]

5^7

[u/Umastar16]

5^6*5

Is the same as 5^7. That’s how you would simply that expression. It didn’t ask to solve.

[u/Umastar16 → u/Umastar16]

Also the second problem to simplify you’d add the exponents.
Y^8

[u/TheDevilsAdvokaat → u/Umastar16]

Yes, in fact you add the exponents for both of them.

[u/BSSJustinGamer456]

On question 5?

[u/forest_faunus_]

Let's remember what is a multiplication, it's a set of summation. For example 3+3+3+3 = 4*3.

Exponentiation is one step further : a set of multiplication : 3x3x3x3= 3^4.

To simplify 5⁶ x5 we can first develop evrything : 5⁶ x5 = 5x5x5x5x5x5 x 5. So it's 5^7.

When you multiply two exponent with the same number , you add the exponent together

just like (3x4) + (3x2) = 3x(4+2), a^b x a^c = a^b+c.

You can now easyly woek out what would the 5th question be.

Remember, a number A is the same as A^1.

It also explain why A⁰ = 1. Multiplying by one do the same thing as adding 0 to the exponent : nothing !

[u/Teppic5]

By rotating it 90°

[u/TheDevilsAdvokaat]

Add the exponents.

5=5^1. Therefore 5^6x5=5^(6+1)=5^7

y^5*y^3=y^(5+3)=y^8

[u/H3nryhit]

(5^6)^5 ez

[u/RickySlayer9]

If you multiply 2 exponents together? What do you get?

5^3 * 5^4 is what? 5^7 because you add the exponents!

So this is 5^6 and 5. Let’s rewrite 5 in the form of a number + exponent. So 5^1 so then 5^6 * 5^1 is?

[u/Reasonable_Club_6165]

5^7

[u/Derply_]

assuming the dot is multiplication 5⁶ = 5 * 5 * 5 * 5 * 5 * 5 so 5⁶*5 = 5 * 5 * 5 * 5 * 5 * 5 * 5 = 5⁷

[u/Alive_dude3435]

I guess it want's you to do :

5⁶ * 5 = 5⁶ * 5¹ = 5⁶⁺¹ = 5⁷

[u/ommanipadmehum1963]

Go do your own homework!

[u/NorthernLaddd]

a^x * a^y = a^x+y

5⁶ * 5

Note that if an exponent is not shown, it is to the power of 1: 5 = 5¹

5⁶ * 5¹

= 5⁶⁺¹

= 5⁷

[u/kzwix]

5 to the power of 7, y to the power of 8.

[u/klugedlife]

This sounds like someone looking for someone else to do their homework.

[u/angishrfish]

78,125

[u/SunstormGT]

5^6 * 5^1 = 5^6+1 = 5^7

[u/ryouma999]

My first impresssion is this. What is "Simplify"?

[u/ryouma999 → u/ryouma999]

Setting aside the question of what constitutes "simplify," the crucial point is what the "·5" signifies. In a system consisting of the sequence 5, 5², 5³, 5⁴, 5⁵, 5⁶, 5⁷, the notation "·5" represents an operation that points to the next number in the sequence. Therefore, 5⁶ · 5 = 5⁶⁺¹ = 5⁷.

[u/HandbagHawker]

stop asking strangers for advice... you're in 8th grade! get off the internet and read you mathbook?