Solve frac{(m^{-2})^{2}(ps)^{2}}{(m^4)^3(p^-3)^3}

$$\frac { ( m ^ { - 2 } ) ^ { 2 } ( p s ) ^ { 2 } } { ( m ^ { 4 } ) ^ { 3 } ( p ^ { - 3 } ) ^ { 3 } }$$

Evaluate

$$\frac{s^{2}p^{11}}{m^{16}}$$

Solution Steps

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

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

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

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

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

$$\frac{m^{-4}\left(ps\right)^{2}}{m^{12}p^{-9}}$$

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

$$\frac{\left(ps\right)^{2}}{p^{-9}m^{16}}$$

Expand \left(ps\right)^{2}.

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

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

$$\frac{s^{2}p^{11}}{m^{16}}$$

Expand

$$\frac{s^{2}p^{11}}{m^{16}}$$

Solution Steps

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

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

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

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

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

$$\frac{m^{-4}\left(ps\right)^{2}}{m^{12}p^{-9}}$$

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

$$\frac{\left(ps\right)^{2}}{p^{-9}m^{16}}$$

Expand \left(ps\right)^{2}.

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

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

$$\frac{s^{2}p^{11}}{m^{16}}$$