Solve (g^{4}h^-2)^5(g^7h^6)

$$( g ^ { 4 } h ^ { - 2 } ) ^ { 5 } ( g ^ { 7 } h ^ { 6 } )$$

Evaluate

$$\frac{g^{27}}{h^{4}}$$

Solution Steps

Expand \left(g^{4}h^{-2}\right)^{5}.

$$\left(g^{4}\right)^{5}\left(h^{-2}\right)^{5}g^{7}h^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$g^{20}\left(h^{-2}\right)^{5}g^{7}h^{6}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$g^{20}h^{-10}g^{7}h^{6}$$

To multiply powers of the same base, add their exponents. Add 20 and 7 to get 27.

$$g^{27}h^{-10}h^{6}$$

To multiply powers of the same base, add their exponents. Add -10 and 6 to get -4.

$$g^{27}h^{-4}$$

Expand

$$\frac{g^{27}}{h^{4}}$$

Solution Steps

Expand \left(g^{4}h^{-2}\right)^{5}.

$$\left(g^{4}\right)^{5}\left(h^{-2}\right)^{5}g^{7}h^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$g^{20}\left(h^{-2}\right)^{5}g^{7}h^{6}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 5 to get -10.

$$g^{20}h^{-10}g^{7}h^{6}$$

To multiply powers of the same base, add their exponents. Add 20 and 7 to get 27.

$$g^{27}h^{-10}h^{6}$$

To multiply powers of the same base, add their exponents. Add -10 and 6 to get -4.

$$g^{27}h^{-4}$$