contestada

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.

Respuesta :

gmany

Answer:

A. a^14 divided by -4

Step-by-step explanation:

[tex](-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}=\dfrac{1}{x^n}\\\\=-\dfrac{1}{2^2}a^{14}\\\\=-\dfrac{a^{14}}{4}[/tex]