Solve left(m^-2right)^2left(p5right)^2/{left(m^4right)^3{left({p}^-3right)}^3}

$$\frac{ { \left( { m }^{ -2 } \right) }^{ 2 } { \left(p5 \right) }^{ 2 } }{ { \left( { m }^{ 4 } \right) }^{ 3 } { \left( { p }^{ -3 } \right) }^{ 3 } }$$

Evaluate

$$\frac{p_{5}^{2}p^{9}}{m^{16}}$$

Solution Steps

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

$$\frac{m^{-4}p_{5}^{2}}{\left(m^{4}\right)^{3}\left(p^{-3}\right)^{3}}$$

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

$$\frac{m^{-4}p_{5}^{2}}{m^{12}\left(p^{-3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{m^{-4}p_{5}^{2}}{m^{12}p^{-9}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{p_{5}^{2}}{p^{-9}m^{16}}$$

Differentiate w.r.t. p_5

$$\frac{2p_{5}p^{9}}{m^{16}}$$