Question

PLEASE HELP ME!

Please simplify this equation.

(-4a^2) (2a^-3)^-4

The options are:

A. a^14 divided by -4

B. 1 divided by -4a^10

C. -4a^10

D. -64a^14

By the way, when the symbol, ^, is behind a number, it means that the number in front of it is an exponent.

Answer 1

A. a^14 divided by -4

Explanation:

`(-4a^2)(2a^(-3))^(-4)\qquad\text{use}\ (xy)^n=x^ny^n\ \text{and}\ (x^n)^m=x^(nm)\\\\=(-4a^2)\bigg(2^(-4)a^((-3)(-4))\bigg)\qquad\text{use}\ 4=2^2\\\\=(-2^2a^2)(2^(-4)a^(12))\\\\=-(2^2)(2^(-4))(a^2a^(12))\qquad\text{use}\ x^nx^m=x^(n+m)\\\\=-2^(2+(-4))a^(2+12)\\\\=-2^(-2)a^(14)\qquad\text{use}\ x^(-n)=(1)/(x^n)\\\\=-(1)/(2^2)a^(14)\\\\=-(a^(14))/(4)`