Question

Can someone help me out please, thank you.

Answer 1

Here are a few rules about exponents you should know:

1. Multiplying exponents of the same base: $x^m*x^n=x^{m+n}$
2. Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
3. Powering a power to a power: $(x^m)^n=x^{m*n}$
4. Converting a negative exponent into a positive one: $x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m$

Firstly, multiply the y bases: $\frac{z^5}{(-y^{-4}y^{-1}x^3)^{-3}}=\frac{z^5}{(-y^{-4+-1}x^3)^{-3}}=\frac{z^5}{(-y^{-5}x^3)^{-3}}$

Next, solve the power: $\frac{z^5}{(-y^{-5}x^3)^{-3}}=\frac{z^5}{-y^{-5*-3}x^{3*-3}}=\frac{z^5}{-y^{15}x^{-9}}$

Finally, convert the negative exponent into a positive one and your final answer will be: $-\frac{z^5x^9}{y^{15}}$