Solve (2a/p^2q^3)^4

$$( \frac { 2 a } { p ^ { 2 } q ^ { 3 } } ) ^ { 4 }$$

Evaluate

$$\frac{16a^{4}}{p^{8}q^{12}}$$

Solution Steps

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

$$\frac{\left(2a\right)^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

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

$$\frac{2^{4}a^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

Expand \left(p^{2}q^{3}\right)^{4}.

$$\frac{16a^{4}}{\left(p^{2}\right)^{4}\left(q^{3}\right)^{4}}$$

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

$$\frac{16a^{4}}{p^{8}\left(q^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{16a^{4}}{p^{8}q^{12}}$$

Expand

$$\frac{16a^{4}}{p^{8}q^{12}}$$

Solution Steps

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

$$\frac{\left(2a\right)^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

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

$$\frac{2^{4}a^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{4}}{\left(p^{2}q^{3}\right)^{4}}$$

Expand \left(p^{2}q^{3}\right)^{4}.

$$\frac{16a^{4}}{\left(p^{2}\right)^{4}\left(q^{3}\right)^{4}}$$

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

$$\frac{16a^{4}}{p^{8}\left(q^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{16a^{4}}{p^{8}q^{12}}$$