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

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

Evaluate

$$\frac{p^{15}}{64}$$

Solution Steps

Cancel out p^{2} in both numerator and denominator.

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

To raise \frac{p^{5}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{p^{15}}{4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{p^{15}}{64}$$

Expand

$$\frac{p^{15}}{64}$$

Solution Steps

Cancel out p^{2} in both numerator and denominator.

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

To raise \frac{p^{5}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{p^{15}}{4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{p^{15}}{64}$$