Solve frac{(4c^{2}d^2)^3}{c^3d^2}

$$\frac { ( 4 c ^ { 2 } d ^ { 2 } ) ^ { 3 } } { c ^ { 3 } d ^ { 2 } }$$

Evaluate

$$64c^{3}d^{4}$$

Solution Steps

Expand \left(4c^{2}d^{2}\right)^{3}.

$$\frac{4^{3}\left(c^{2}\right)^{3}\left(d^{2}\right)^{3}}{c^{3}d^{2}}$$

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

$$\frac{4^{3}c^{6}\left(d^{2}\right)^{3}}{c^{3}d^{2}}$$

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

$$\frac{4^{3}c^{6}d^{6}}{c^{3}d^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64c^{6}d^{6}}{c^{3}d^{2}}$$

Cancel out d^{2}c^{3} in both numerator and denominator.

$$64c^{3}d^{4}$$

Expand

$$64c^{3}d^{4}$$

Solution Steps

Expand \left(4c^{2}d^{2}\right)^{3}.

$$\frac{4^{3}\left(c^{2}\right)^{3}\left(d^{2}\right)^{3}}{c^{3}d^{2}}$$

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

$$\frac{4^{3}c^{6}\left(d^{2}\right)^{3}}{c^{3}d^{2}}$$

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

$$\frac{4^{3}c^{6}d^{6}}{c^{3}d^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64c^{6}d^{6}}{c^{3}d^{2}}$$

Cancel out d^{2}c^{3} in both numerator and denominator.

$$64c^{3}d^{4}$$