Fully simplify

Question

(z^-3\cdotz^-7)^-4

Answer 1

To fully simplify (z^-3 · z^-7)^-4, we need to apply the rules of exponents.

First, we can multiply the exponents inside the parentheses by -4:
(z^-3 · z^-7)^-4 = z^(-3 * -4) · z^(-7 * -4)

Simplifying the exponents further:
= z^12 · z^28

Now, we can combine these two exponents by adding them together:
= z^(12 + 28)

= z^40

Therefore, the fully simplified expression is z^40.