Solve (4p^3q^5)/(2pq^2)^6=

$$\frac { ( 4 p ^ { 3 } q ^ { 5 } ) } { ( 2 p q ^ { 2 } ) ^ { 6 } } =$$

Evaluate

$$\frac{1}{16p^{3}q^{7}}$$

Solution Steps

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

$$\frac{4p^{3}q^{5}}{2^{6}p^{6}\left(q^{2}\right)^{6}}$$

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

$$\frac{4p^{3}q^{5}}{2^{6}p^{6}q^{12}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{4p^{3}q^{5}}{64p^{6}q^{12}}$$

Cancel out 4p^{3}q^{5} in both numerator and denominator.

$$\frac{1}{16p^{3}q^{7}}$$

Expand

$$\frac{1}{16p^{3}q^{7}}$$

Solution Steps

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

$$\frac{4p^{3}q^{5}}{2^{6}p^{6}\left(q^{2}\right)^{6}}$$

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

$$\frac{4p^{3}q^{5}}{2^{6}p^{6}q^{12}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{4p^{3}q^{5}}{64p^{6}q^{12}}$$

Cancel out 4p^{3}q^{5} in both numerator and denominator.

$$\frac{1}{16p^{3}q^{7}}$$