Question

Which expression is equivalent?

Answer 1

`\large\boxed{(g^(15))/(8h^6)}`

Explanation:

`(\left(2g^5\right)^3)/(\left(4h^2\right)^3)=(\left(2g^5\right)^3)/(\left(2^2h^2\right)^3)\qquad\text{use}\ (a^n)^m=a^(nm)\ \text{and}\ (ab)^n=a^nb^n\\\\=(2^3g^((5)(3)))/(2^((2)(3))h^((2)(3)))=(2^3g^(15))/(2^6h^6)=(2^3g^(15))/(2^(3+3)h^6)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=(2^3g^(15))/(2^3\cdot2^3h^6)=(g^(15))/(8h^6)`