Solve (2p^7)^2/(4p^2)^3

$$\frac { ( 2 p ^ { 7 } ) ^ { 2 } } { ( 4 p ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$\frac{p^{8}}{16}$$

Solution Steps

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

$$\frac{2^{2}\left(p^{7}\right)^{2}}{\left(4p^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{2^{2}p^{14}}{\left(4p^{2}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4p^{14}}{\left(4p^{2}\right)^{3}}$$

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

$$\frac{4p^{14}}{4^{3}\left(p^{2}\right)^{3}}$$

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

$$\frac{4p^{14}}{4^{3}p^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{4p^{14}}{64p^{6}}$$

Cancel out 4p^{6} in both numerator and denominator.

$$\frac{p^{8}}{16}$$

Expand

$$\frac{p^{8}}{16}$$

Solution Steps

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

$$\frac{2^{2}\left(p^{7}\right)^{2}}{\left(4p^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{2^{2}p^{14}}{\left(4p^{2}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4p^{14}}{\left(4p^{2}\right)^{3}}$$

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

$$\frac{4p^{14}}{4^{3}\left(p^{2}\right)^{3}}$$

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

$$\frac{4p^{14}}{4^{3}p^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{4p^{14}}{64p^{6}}$$

Cancel out 4p^{6} in both numerator and denominator.

$$\frac{p^{8}}{16}$$