Question

Which expression is equivalent?

Answer 1

Answer:

$\large\boxed{\dfrac{g^{15}}{8h^6}}$

Step-by-step explanation:

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