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

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

Evaluate

$$16a^{2}b^{9}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{2a^{2}}{2^{-3}b^{-9}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{2a^{2}}{\frac{1}{8}b^{-9}}$$

Expand

$$16a^{2}b^{9}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{2a^{2}}{2^{-3}b^{-9}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{2a^{2}}{\frac{1}{8}b^{-9}}$$