Solve -frac{2m^{4}p^{2}q^{3}*-2m^{2}q^{-3}*-2m^{-4}p^{4}q^{-3}}{(m^0p^4q^2)^4}

$$- \frac { 2 m ^ { 4 } p ^ { 2 } q ^ { 3 } \cdot - 2 m ^ { 2 } q ^ { - 3 } \cdot - 2 m ^ { - 4 } p ^ { 4 } q ^ { - 3 } } { ( m ^ { 0 } p ^ { 4 } q ^ { 2 } ) ^ { 4 } }$$

Evaluate

$$-\frac{8m^{2}}{p^{10}q^{11}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-\frac{2m^{6}p^{2}q^{3}\left(-2\right)q^{-3}\left(-2\right)m^{-4}p^{4}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and -4 to get 2.

$$-\frac{2m^{2}p^{2}q^{3}\left(-2\right)q^{-3}\left(-2\right)p^{4}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-\frac{2m^{2}p^{6}q^{3}\left(-2\right)q^{-3}\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply q^{3} and q^{-3} to get 1.

$$-\frac{2m^{2}p^{6}\left(-2\right)\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply 2 and -2 to get -4.

$$-\frac{-4m^{2}p^{6}\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply -4 and -2 to get 8.

$$-\frac{8m^{2}p^{6}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Calculate m to the power of 0 and get 1.

$$-\frac{8m^{2}p^{6}q^{-3}}{\left(1p^{4}q^{2}\right)^{4}}$$

Expand \left(1p^{4}q^{2}\right)^{4}.

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}\left(p^{4}\right)^{4}\left(q^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}p^{16}\left(q^{2}\right)^{4}}$$

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

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}p^{16}q^{8}}$$

Calculate 1 to the power of 4 and get 1.

$$-\frac{8m^{2}p^{6}q^{-3}}{1p^{16}q^{8}}$$

Cancel out p^{6} in both numerator and denominator.

$$-\frac{8q^{-3}m^{2}}{q^{8}p^{10}}$$

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

$$-\frac{8m^{2}}{p^{10}q^{11}}$$

Expand

$$-\frac{8m^{2}}{p^{10}q^{11}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-\frac{2m^{6}p^{2}q^{3}\left(-2\right)q^{-3}\left(-2\right)m^{-4}p^{4}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and -4 to get 2.

$$-\frac{2m^{2}p^{2}q^{3}\left(-2\right)q^{-3}\left(-2\right)p^{4}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-\frac{2m^{2}p^{6}q^{3}\left(-2\right)q^{-3}\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply q^{3} and q^{-3} to get 1.

$$-\frac{2m^{2}p^{6}\left(-2\right)\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply 2 and -2 to get -4.

$$-\frac{-4m^{2}p^{6}\left(-2\right)q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Multiply -4 and -2 to get 8.

$$-\frac{8m^{2}p^{6}q^{-3}}{\left(m^{0}p^{4}q^{2}\right)^{4}}$$

Calculate m to the power of 0 and get 1.

$$-\frac{8m^{2}p^{6}q^{-3}}{\left(1p^{4}q^{2}\right)^{4}}$$

Expand \left(1p^{4}q^{2}\right)^{4}.

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}\left(p^{4}\right)^{4}\left(q^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}p^{16}\left(q^{2}\right)^{4}}$$

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

$$-\frac{8m^{2}p^{6}q^{-3}}{1^{4}p^{16}q^{8}}$$

Calculate 1 to the power of 4 and get 1.

$$-\frac{8m^{2}p^{6}q^{-3}}{1p^{16}q^{8}}$$

Cancel out p^{6} in both numerator and denominator.

$$-\frac{8q^{-3}m^{2}}{q^{8}p^{10}}$$

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

$$-\frac{8m^{2}}{p^{10}q^{11}}$$