Solve (4b^2/c^-5)^-3

$$( \frac { 4 b ^ { 2 } } { c ^ { - 5 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{64b^{6}c^{15}}$$

Solution Steps

To raise \frac{4b^{2}}{c^{-5}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{\left(4b^{2}\right)^{-3}}{c^{15}}$$

Expand \left(4b^{2}\right)^{-3}.

$$\frac{4^{-3}\left(b^{2}\right)^{-3}}{c^{15}}$$

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

$$\frac{4^{-3}b^{-6}}{c^{15}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{64}b^{-6}}{c^{15}}$$

Expand

$$\frac{1}{64b^{6}c^{15}}$$

Solution Steps

To raise \frac{4b^{2}}{c^{-5}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{\left(4b^{2}\right)^{-3}}{c^{15}}$$

Expand \left(4b^{2}\right)^{-3}.

$$\frac{4^{-3}\left(b^{2}\right)^{-3}}{c^{15}}$$

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

$$\frac{4^{-3}b^{-6}}{c^{15}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{64}b^{-6}}{c^{15}}$$