Question

(2/7 r^5 s^3)^2

Simplify? I've tried problems similar to this but the website keeps marking it wrong

Answer 1

is that \[(\frac{2}{7}r^5s^3)^2\]or something else?

Answer 2

Yeah, I couldn't get it like that

Answer 3

Okay, what have you tried as an answer?

Answer 4

Let's see if we can identify where you are going astray...

Answer 5

\[(\frac{ 2 }{ 7 }r^5s^3)(\frac{ 2 }{ 7 }r^5s^3)\]

Answer 6

I got 4/49 r^25 s^9

Answer 7

Astray?

Answer 8

Ooh I see when you expanded you multiplied the variables

Answer 9

The problem is your exponents.

(a^n)^m=a^(nm). You were squaring the exponents themselves.

2/7 ^2=4/49. r^5 ^2=r^10. s^3 ^2=s^6.

Your answer should be
4/49 r^10 s^6

Answer 10

\(\bf \left(\cfrac{2}{7}r^5 s^3\right)^{\color{red}{ 2}}\implies \left(\cfrac{2}{7}\right)^{\color{red}{ 2}}\cdot r^{5\cdot {\color{red}{ 2}}}s^{3\cdot {\color{red}{ 2}}}\implies \cfrac{2^{\color{red}{ 2}}}{7^{\color{red}{ 2}}}\cdot r^{5\cdot {\color{red}{ 2}}}s^{3\cdot {\color{red}{ 2}}}\)

Answer 11

Sorry lost connection, nice job @jdoe0001 :D

Answer 12

Yeah, I got cut off as well.

When multiplying exponentials with the same base, you add the exponents (and subtract for division). This is the same as with logarithms, where when multiplying you add the logarithms, and when dividing you subtract them. Remember that for when you learn about logarithms :-)