Solve (2^3)^-1(4m^3)^2

$$( 2 ^ { 3 } ) ^ { - 1 } ( 4 m ^ { 3 } ) ^ { 2 }$$

Evaluate

$$2m^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$2^{-3}\times \left(4m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times \left(4m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times 4^{2}\left(m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times 4^{2}m^{6}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{8}\times 16m^{6}$$

Multiply \frac{1}{8} and 16 to get 2.

$$2m^{6}$$

Expand

$$2m^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$2^{-3}\times \left(4m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times \left(4m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times 4^{2}\left(m^{3}\right)^{2}$$

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

$$\frac{1}{8}\times 4^{2}m^{6}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{8}\times 16m^{6}$$

Multiply \frac{1}{8} and 16 to get 2.

$$2m^{6}$$