Solve frac{(5gh^{3})^2*3g^3}{8g^7h^4}

$$\frac { ( 5 g h ^ { 3 } ) ^ { 2 } \times 3 g ^ { 3 } } { 8 g ^ { 7 } h ^ { 4 } }$$

Evaluate

$$\frac{75\times \left(\frac{h}{g}\right)^{2}}{8}$$

Solution Steps

Cancel out g^{3} in both numerator and denominator.

$$\frac{3\times \left(5gh^{3}\right)^{2}}{8g^{4}h^{4}}$$

Expand \left(5gh^{3}\right)^{2}.

$$\frac{3\times 5^{2}g^{2}\left(h^{3}\right)^{2}}{8g^{4}h^{4}}$$

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

$$\frac{3\times 5^{2}g^{2}h^{6}}{8g^{4}h^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{3\times 25g^{2}h^{6}}{8g^{4}h^{4}}$$

Multiply 3 and 25 to get 75.

$$\frac{75g^{2}h^{6}}{8g^{4}h^{4}}$$

Cancel out g^{2}h^{4} in both numerator and denominator.

$$\frac{75h^{2}}{8g^{2}}$$

Expand

$$\frac{75\times \left(\frac{h}{g}\right)^{2}}{8}$$

Solution Steps

Cancel out g^{3} in both numerator and denominator.

$$\frac{3\times \left(5gh^{3}\right)^{2}}{8g^{4}h^{4}}$$

Expand \left(5gh^{3}\right)^{2}.

$$\frac{3\times 5^{2}g^{2}\left(h^{3}\right)^{2}}{8g^{4}h^{4}}$$

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

$$\frac{3\times 5^{2}g^{2}h^{6}}{8g^{4}h^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{3\times 25g^{2}h^{6}}{8g^{4}h^{4}}$$

Multiply 3 and 25 to get 75.

$$\frac{75g^{2}h^{6}}{8g^{4}h^{4}}$$

Cancel out g^{2}h^{4} in both numerator and denominator.

$$\frac{75h^{2}}{8g^{2}}$$