Fully simplify

Question

(z^-5\cdotz^9)^8

Answer 1

To fully simplify (z^-5 * z^9)^8, we need to first simplify the expression inside the parentheses and then apply the exponent outside.

Inside the parentheses, we can multiply the two terms with the same base, z. When we multiply terms with the same base, we add their exponents.

So, (z^-5 * z^9) becomes z^(-5 + 9) which becomes z^4.

Now, the expression becomes (z^4)^8. When we raise a term with an exponent to another exponent, we multiply the exponents.

So, (z^4)^8 becomes z^(4 * 8) which becomes z^32.

Therefore, the fully simplified expression is z^32.