Solve frac{(3c^{2})^2(-d^5)}{-45c^7d^3}

$$\frac { ( 3 c ^ { 2 } ) ^ { 2 } ( - d ^ { 5 } ) } { - 45 c ^ { 7 } d ^ { 3 } }$$

Evaluate

$$\frac{d^{2}}{5c^{3}}$$

Solution Steps

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

$$\frac{3^{2}\left(c^{2}\right)^{2}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

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

$$\frac{3^{2}c^{4}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9c^{4}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

Cancel out 9c^{4} in both numerator and denominator.

$$\frac{-d^{5}}{-5c^{3}d^{3}}$$

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

$$\frac{-d^{2}}{-5c^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{d^{2}}{5c^{3}}$$

Expand

$$\frac{d^{2}}{5c^{3}}$$

Solution Steps

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

$$\frac{3^{2}\left(c^{2}\right)^{2}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

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

$$\frac{3^{2}c^{4}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9c^{4}\left(-d^{5}\right)}{-45c^{7}d^{3}}$$

Cancel out 9c^{4} in both numerator and denominator.

$$\frac{-d^{5}}{-5c^{3}d^{3}}$$

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

$$\frac{-d^{2}}{-5c^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{d^{2}}{5c^{3}}$$