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

$$( \frac { 3 m ^ { 3 } } { 4 m ^ { - 4 } } ) ^ { 2 }$$

Evaluate

$$\frac{9m^{14}}{16}$$

Solution Steps

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

$$\left(\frac{3m^{7}}{4}\right)^{2}$$

To raise \frac{3m^{7}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{7}\right)^{2}}{4^{2}}$$

Expand \left(3m^{7}\right)^{2}.

$$\frac{3^{2}\left(m^{7}\right)^{2}}{4^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{3^{2}m^{14}}{4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{14}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9m^{14}}{16}$$

Expand

$$\frac{9m^{14}}{16}$$

Solution Steps

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

$$\left(\frac{3m^{7}}{4}\right)^{2}$$

To raise \frac{3m^{7}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{7}\right)^{2}}{4^{2}}$$

Expand \left(3m^{7}\right)^{2}.

$$\frac{3^{2}\left(m^{7}\right)^{2}}{4^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{3^{2}m^{14}}{4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{14}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9m^{14}}{16}$$