Solve (p^2*p^-5)^2/p^3

$$\frac { ( p ^ { 2 } \times p ^ { - 5 } ) ^ { 2 } } { p ^ { 3 } }$$

Evaluate

$$\frac{1}{p^{9}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -5 to get -3.

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

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

$$\frac{p^{-6}}{p^{3}}$$

Rewrite p^{3} as p^{-6}p^{9}. Cancel out p^{-6} in both numerator and denominator.

$$\frac{1}{p^{9}}$$

Expand

$$\frac{1}{p^{9}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -5 to get -3.

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

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

$$\frac{p^{-6}}{p^{3}}$$

Rewrite p^{3} as p^{-6}p^{9}. Cancel out p^{-6} in both numerator and denominator.

$$\frac{1}{p^{9}}$$