Solve (6)(25k^4/m^8)^2

$$( 6 ) ( \frac { 25 k ^ { 4 } } { m ^ { 8 } } ) ^ { 2 }$$

Evaluate

$$\frac{3750k^{8}}{m^{16}}$$

Solution Steps

To raise \frac{25k^{4}}{m^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$6\times \frac{\left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}}$$

Express 6\times \frac{\left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}} as a single fraction.

$$\frac{6\times \left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}}$$

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

$$\frac{6\times \left(25k^{4}\right)^{2}}{m^{16}}$$

Expand \left(25k^{4}\right)^{2}.

$$\frac{6\times 25^{2}\left(k^{4}\right)^{2}}{m^{16}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{6\times 25^{2}k^{8}}{m^{16}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{6\times 625k^{8}}{m^{16}}$$

Multiply 6 and 625 to get 3750.

$$\frac{3750k^{8}}{m^{16}}$$

Expand

$$\frac{3750k^{8}}{m^{16}}$$

Solution Steps

To raise \frac{25k^{4}}{m^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$6\times \frac{\left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}}$$

Express 6\times \frac{\left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}} as a single fraction.

$$\frac{6\times \left(25k^{4}\right)^{2}}{\left(m^{8}\right)^{2}}$$

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

$$\frac{6\times \left(25k^{4}\right)^{2}}{m^{16}}$$

Expand \left(25k^{4}\right)^{2}.

$$\frac{6\times 25^{2}\left(k^{4}\right)^{2}}{m^{16}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{6\times 25^{2}k^{8}}{m^{16}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{6\times 625k^{8}}{m^{16}}$$

Multiply 6 and 625 to get 3750.

$$\frac{3750k^{8}}{m^{16}}$$