Solve (3np^3/7q^2)^2

$$( \frac { 3 n p ^ { 3 } } { 7 q ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{9n^{2}p^{6}}{49q^{4}}$$

Solution Steps

To raise \frac{3np^{3}}{7q^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3np^{3}\right)^{2}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{3^{2}n^{2}\left(p^{3}\right)^{2}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{3^{2}n^{2}p^{6}}{\left(7q^{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9n^{2}p^{6}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{9n^{2}p^{6}}{7^{2}\left(q^{2}\right)^{2}}$$

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

$$\frac{9n^{2}p^{6}}{7^{2}q^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{9n^{2}p^{6}}{49q^{4}}$$

Expand

$$\frac{9n^{2}p^{6}}{49q^{4}}$$

Solution Steps

To raise \frac{3np^{3}}{7q^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3np^{3}\right)^{2}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{3^{2}n^{2}\left(p^{3}\right)^{2}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{3^{2}n^{2}p^{6}}{\left(7q^{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9n^{2}p^{6}}{\left(7q^{2}\right)^{2}}$$

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

$$\frac{9n^{2}p^{6}}{7^{2}\left(q^{2}\right)^{2}}$$

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

$$\frac{9n^{2}p^{6}}{7^{2}q^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{9n^{2}p^{6}}{49q^{4}}$$