Solve (3m^2r^3/4p^-8)^2=

$$( \frac { 3 m ^ { 2 } r ^ { 3 } } { 4 p ^ { - 8 } } ) ^ { 2 } =$$

Evaluate

$$\frac{9m^{4}r^{6}p^{16}}{16}$$

Solution Steps

To raise \frac{3m^{2}r^{3}}{4p^{-8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{2}r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

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

$$\frac{3^{2}\left(m^{2}\right)^{2}\left(r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}m^{4}\left(r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

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

$$\frac{3^{2}m^{4}r^{6}}{\left(4p^{-8}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{4}r^{6}}{\left(4p^{-8}\right)^{2}}$$

Expand \left(4p^{-8}\right)^{2}.

$$\frac{9m^{4}r^{6}}{4^{2}\left(p^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 2 to get -16.

$$\frac{9m^{4}r^{6}}{4^{2}p^{-16}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9m^{4}r^{6}}{16p^{-16}}$$

Expand

$$\frac{9m^{4}r^{6}p^{16}}{16}$$

Solution Steps

To raise \frac{3m^{2}r^{3}}{4p^{-8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{2}r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

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

$$\frac{3^{2}\left(m^{2}\right)^{2}\left(r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}m^{4}\left(r^{3}\right)^{2}}{\left(4p^{-8}\right)^{2}}$$

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

$$\frac{3^{2}m^{4}r^{6}}{\left(4p^{-8}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{4}r^{6}}{\left(4p^{-8}\right)^{2}}$$

Expand \left(4p^{-8}\right)^{2}.

$$\frac{9m^{4}r^{6}}{4^{2}\left(p^{-8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and 2 to get -16.

$$\frac{9m^{4}r^{6}}{4^{2}p^{-16}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9m^{4}r^{6}}{16p^{-16}}$$