Solve frac{(2m^{-3}n^{2}p^{4})^-2}{6m^4n^-5p^3}

$$\frac { ( 2 m ^ { - 3 } n ^ { 2 } p ^ { 4 } ) ^ { - 2 } } { 6 m ^ { 4 } n ^ { - 5 } p ^ { 3 } }$$

Evaluate

$$\frac{nm^{2}}{24p^{11}}$$

Solution Steps

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

$$\frac{2^{-2}\left(m^{-3}\right)^{-2}\left(n^{2}\right)^{-2}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{2^{-2}m^{6}\left(n^{2}\right)^{-2}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{2^{-2}m^{6}n^{-4}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{2^{-2}m^{6}n^{-4}p^{-8}}{6m^{4}n^{-5}p^{3}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}m^{6}n^{-4}p^{-8}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{\frac{1}{4}p^{-8}n^{-4}m^{2}}{6n^{-5}p^{3}}$$

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

$$\frac{\frac{1}{4}p^{-8}n^{1}m^{2}}{6p^{3}}$$

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

$$\frac{\frac{1}{4}n^{1}m^{2}}{6p^{11}}$$

Calculate n to the power of 1 and get n.

$$\frac{\frac{1}{4}nm^{2}}{6p^{11}}$$

Expand

$$\frac{nm^{2}}{24p^{11}}$$

Solution Steps

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

$$\frac{2^{-2}\left(m^{-3}\right)^{-2}\left(n^{2}\right)^{-2}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{2^{-2}m^{6}\left(n^{2}\right)^{-2}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{2^{-2}m^{6}n^{-4}\left(p^{4}\right)^{-2}}{6m^{4}n^{-5}p^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{2^{-2}m^{6}n^{-4}p^{-8}}{6m^{4}n^{-5}p^{3}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}m^{6}n^{-4}p^{-8}}{6m^{4}n^{-5}p^{3}}$$

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

$$\frac{\frac{1}{4}p^{-8}n^{-4}m^{2}}{6n^{-5}p^{3}}$$

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

$$\frac{\frac{1}{4}p^{-8}n^{1}m^{2}}{6p^{3}}$$

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

$$\frac{\frac{1}{4}n^{1}m^{2}}{6p^{11}}$$

Calculate n to the power of 1 and get n.

$$\frac{\frac{1}{4}nm^{2}}{6p^{11}}$$