Solve (b^-3/2a^6)^-5

$$( \frac { b ^ { - 3 } } { 2 a ^ { 6 } } ) ^ { - 5 }$$

Evaluate

$$32b^{15}a^{30}$$

Solution Steps

To raise \frac{b^{-3}}{2a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{-3}\right)^{-5}}{\left(2a^{6}\right)^{-5}}$$

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

$$\frac{b^{15}}{\left(2a^{6}\right)^{-5}}$$

Expand \left(2a^{6}\right)^{-5}.

$$\frac{b^{15}}{2^{-5}\left(a^{6}\right)^{-5}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -5 to get -30.

$$\frac{b^{15}}{2^{-5}a^{-30}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{b^{15}}{\frac{1}{32}a^{-30}}$$

Expand

$$32b^{15}a^{30}$$

Solution Steps

To raise \frac{b^{-3}}{2a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{-3}\right)^{-5}}{\left(2a^{6}\right)^{-5}}$$

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

$$\frac{b^{15}}{\left(2a^{6}\right)^{-5}}$$

Expand \left(2a^{6}\right)^{-5}.

$$\frac{b^{15}}{2^{-5}\left(a^{6}\right)^{-5}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -5 to get -30.

$$\frac{b^{15}}{2^{-5}a^{-30}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{b^{15}}{\frac{1}{32}a^{-30}}$$