Solve frac{-4q^{5}}{(2q^2r^2)^4(-7q^6)}

$$\frac { - 4 q ^ { 5 } } { ( 2 q ^ { 2 } r ^ { 2 } ) ^ { 4 } ( - 7 q ^ { 6 } ) }$$

Evaluate

$$\frac{1}{28r^{8}q^{9}}$$

Solution Steps

Cancel out q^{5} in both numerator and denominator.

$$\frac{-4}{-7q\times \left(2q^{2}r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}\left(q^{2}\right)^{4}\left(r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}q^{8}\left(r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}q^{8}r^{8}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-4}{-7q\times 16q^{8}r^{8}}$$

Multiply -7 and 16 to get -112.

$$\frac{-4}{-112qq^{8}r^{8}}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{-4}{-112q^{9}r^{8}}$$

Expand

$$\frac{1}{28r^{8}q^{9}}$$

Solution Steps

Cancel out q^{5} in both numerator and denominator.

$$\frac{-4}{-7q\times \left(2q^{2}r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}\left(q^{2}\right)^{4}\left(r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}q^{8}\left(r^{2}\right)^{4}}$$

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

$$\frac{-4}{-7q\times 2^{4}q^{8}r^{8}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-4}{-7q\times 16q^{8}r^{8}}$$

Multiply -7 and 16 to get -112.

$$\frac{-4}{-112qq^{8}r^{8}}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{-4}{-112q^{9}r^{8}}$$