Solve (6w^5/7p^6r^3)^2

$$( \frac { 6 w ^ { 5 } } { 7 p ^ { 6 } r ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{36w^{10}}{49r^{6}p^{12}}$$

Solution Steps

To raise \frac{6w^{5}}{7p^{6}r^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6w^{5}\right)^{2}}{\left(7p^{6}r^{3}\right)^{2}}$$

Expand \left(6w^{5}\right)^{2}.

$$\frac{6^{2}\left(w^{5}\right)^{2}}{\left(7p^{6}r^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{6^{2}w^{10}}{\left(7p^{6}r^{3}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36w^{10}}{\left(7p^{6}r^{3}\right)^{2}}$$

Expand \left(7p^{6}r^{3}\right)^{2}.

$$\frac{36w^{10}}{7^{2}\left(p^{6}\right)^{2}\left(r^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{36w^{10}}{7^{2}p^{12}\left(r^{3}\right)^{2}}$$

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

$$\frac{36w^{10}}{7^{2}p^{12}r^{6}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{36w^{10}}{49p^{12}r^{6}}$$

Expand

$$\frac{36w^{10}}{49r^{6}p^{12}}$$

Solution Steps

To raise \frac{6w^{5}}{7p^{6}r^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6w^{5}\right)^{2}}{\left(7p^{6}r^{3}\right)^{2}}$$

Expand \left(6w^{5}\right)^{2}.

$$\frac{6^{2}\left(w^{5}\right)^{2}}{\left(7p^{6}r^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{6^{2}w^{10}}{\left(7p^{6}r^{3}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36w^{10}}{\left(7p^{6}r^{3}\right)^{2}}$$

Expand \left(7p^{6}r^{3}\right)^{2}.

$$\frac{36w^{10}}{7^{2}\left(p^{6}\right)^{2}\left(r^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{36w^{10}}{7^{2}p^{12}\left(r^{3}\right)^{2}}$$

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

$$\frac{36w^{10}}{7^{2}p^{12}r^{6}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{36w^{10}}{49p^{12}r^{6}}$$