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

$$( \frac { m ^ { - 3 } } { 4 m ^ { - 1 } } ) ^ { 3 }$$

Evaluate

$$\frac{1}{64m^{6}}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{1}{4m^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of 3 and get 1.

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

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

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

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

$$\frac{1}{4^{3}m^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{1}{64m^{6}}$$

Expand

$$\frac{1}{64m^{6}}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{1}{4m^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of 3 and get 1.

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

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

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

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

$$\frac{1}{4^{3}m^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{1}{64m^{6}}$$