Solve (9g^3/8h^2)^2

$$( \frac { 9 g ^ { 3 } } { 8 h ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{81g^{6}}{64h^{4}}$$

Solution Steps

To raise \frac{9g^{3}}{8h^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9g^{3}\right)^{2}}{\left(8h^{2}\right)^{2}}$$

Expand \left(9g^{3}\right)^{2}.

$$\frac{9^{2}\left(g^{3}\right)^{2}}{\left(8h^{2}\right)^{2}}$$

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

$$\frac{9^{2}g^{6}}{\left(8h^{2}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81g^{6}}{\left(8h^{2}\right)^{2}}$$

Expand \left(8h^{2}\right)^{2}.

$$\frac{81g^{6}}{8^{2}\left(h^{2}\right)^{2}}$$

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

$$\frac{81g^{6}}{8^{2}h^{4}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{81g^{6}}{64h^{4}}$$

Expand

$$\frac{81g^{6}}{64h^{4}}$$

Solution Steps

To raise \frac{9g^{3}}{8h^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9g^{3}\right)^{2}}{\left(8h^{2}\right)^{2}}$$

Expand \left(9g^{3}\right)^{2}.

$$\frac{9^{2}\left(g^{3}\right)^{2}}{\left(8h^{2}\right)^{2}}$$

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

$$\frac{9^{2}g^{6}}{\left(8h^{2}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81g^{6}}{\left(8h^{2}\right)^{2}}$$

Expand \left(8h^{2}\right)^{2}.

$$\frac{81g^{6}}{8^{2}\left(h^{2}\right)^{2}}$$

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

$$\frac{81g^{6}}{8^{2}h^{4}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{81g^{6}}{64h^{4}}$$