Question

how to simplify (4x^2)^3 divided by 2x^7?

Answer 1

Given the expression:

$\frac{(4x^2)^3}{2x^7}$

so simplify, we have to use the following general rules for exponents:

$\begin{gathered} (a^n)^m=a^{n\cdot m} \\ \frac{a^n}{a^m}=a^{n-m} \end{gathered}$

then, in this case we have the following:

$\frac{(4x^2)^3}{2x^7}=\frac{4^3x^{2\cdot3}}{2x^7}=\frac{64x^6}{2x^7}=\frac{64}{2}x^{6-7}=32x^{-1}^{}$

therefore, the simplifide expression is 32x^(-1)