Question

(1/2x^2)^3(-8x^3)^2

Answer 1

Okay Zechariah, if I've read correctly, you have this: \[\left( \frac{1}{2x^2} \right)^3(-8x^3)^2\]You need to use power laws to simplify. If you have\[\left( \frac{a}{b} \right)^n\]this will be equal to\[\frac{a^3}{b^3}\]Also, if you have\[(ab)^n\]this will be equal to\[a^nb^n\]and if you have\[(a^m)^n\]this will be equal to \[a^{mn}\]You can apply these two laws to what you've got. So,\[\left( \frac{1}{2x^2} \right)^3=\frac{1}{(2x^2)^3}=\frac{1}{2^3(x^2)^3}=\frac{1}{8x^6}\]and \[(-8x^3)^2=(-1)^2(8)^2(x^3)^2=64x^6\]So your expression becomes\[\left( \frac{1}{2x^2} \right)^3(-8x^3)^2=\frac{1}{8x^6} \times 64x^6=\frac{64x^6}{8x^6}=\frac{8 \times 8 x^6}{8x^6}=8\]

Answer 2

Above I said\[\left( \frac{a}{b} \right)^n=\frac{a^3}{b^3}\]It doesn't; it's a typo. It should read,\[\left( \frac{a}{b} \right)^n=\frac{a^n}{b^n}\]

Answer 3

PS: I like your "About Me" statement :) You have the right attitude.

Answer 4

Thank you