Solve frac{(2g^{3}h^{-2})^2}{(g^2h^0)^-3}

$$\frac { ( 2 g ^ { 3 } h ^ { - 2 } ) ^ { 2 } } { ( g ^ { 2 } h ^ { 0 } ) ^ { - 3 } }$$

Evaluate

$$\frac{4g^{12}}{h^{4}}$$

Solution Steps

Expand \left(2g^{3}h^{-2}\right)^{2}.

$$\frac{2^{2}\left(g^{3}\right)^{2}\left(h^{-2}\right)^{2}}{\left(g^{2}h^{0}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}g^{6}\left(h^{-2}\right)^{2}}{\left(g^{2}h^{0}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{2^{2}g^{6}h^{-4}}{\left(g^{2}h^{0}\right)^{-3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}h^{0}\right)^{-3}}$$

Calculate h to the power of 0 and get 1.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}\times 1\right)^{-3}}$$

Expand \left(g^{2}\times 1\right)^{-3}.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}\right)^{-3}\times 1^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{4g^{6}h^{-4}}{g^{-6}\times 1^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{4g^{6}h^{-4}}{g^{-6}\times 1}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4h^{-4}g^{12}$$

Expand

$$\frac{4g^{12}}{h^{4}}$$

Solution Steps

Expand \left(2g^{3}h^{-2}\right)^{2}.

$$\frac{2^{2}\left(g^{3}\right)^{2}\left(h^{-2}\right)^{2}}{\left(g^{2}h^{0}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{2}g^{6}\left(h^{-2}\right)^{2}}{\left(g^{2}h^{0}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{2^{2}g^{6}h^{-4}}{\left(g^{2}h^{0}\right)^{-3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}h^{0}\right)^{-3}}$$

Calculate h to the power of 0 and get 1.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}\times 1\right)^{-3}}$$

Expand \left(g^{2}\times 1\right)^{-3}.

$$\frac{4g^{6}h^{-4}}{\left(g^{2}\right)^{-3}\times 1^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{4g^{6}h^{-4}}{g^{-6}\times 1^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{4g^{6}h^{-4}}{g^{-6}\times 1}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4h^{-4}g^{12}$$