Solve frac{(12c^{3}d^7)^2}{18c^8d^10}

$$\frac { ( 12 c ^ { 3 } d ^ { 7 } ) ^ { 2 } } { 18 c ^ { 8 } d ^ { 10 } }$$

Evaluate

$$\frac{8d^{4}}{c^{2}}$$

Solution Steps

Expand \left(12c^{3}d^{7}\right)^{2}.

$$\frac{12^{2}\left(c^{3}\right)^{2}\left(d^{7}\right)^{2}}{18c^{8}d^{10}}$$

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

$$\frac{12^{2}c^{6}\left(d^{7}\right)^{2}}{18c^{8}d^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{12^{2}c^{6}d^{14}}{18c^{8}d^{10}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144c^{6}d^{14}}{18c^{8}d^{10}}$$

Cancel out 18c^{6}d^{10} in both numerator and denominator.

$$\frac{8d^{4}}{c^{2}}$$

Expand

$$\frac{8d^{4}}{c^{2}}$$

Solution Steps

Expand \left(12c^{3}d^{7}\right)^{2}.

$$\frac{12^{2}\left(c^{3}\right)^{2}\left(d^{7}\right)^{2}}{18c^{8}d^{10}}$$

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

$$\frac{12^{2}c^{6}\left(d^{7}\right)^{2}}{18c^{8}d^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{12^{2}c^{6}d^{14}}{18c^{8}d^{10}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144c^{6}d^{14}}{18c^{8}d^{10}}$$

Cancel out 18c^{6}d^{10} in both numerator and denominator.

$$\frac{8d^{4}}{c^{2}}$$