Solve (4p/q)^-2div(1/2q)^3

$$( \frac { 4 p } { q } ) ^ { - 2 } \div ( \frac { 1 } { 2 } q ) ^ { 3 }$$

Evaluate

$$\frac{1}{2qp^{2}}$$

Solution Steps

To raise \frac{4p}{q} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(\frac{1}{2}q\right)^{3}.

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

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

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

Express \frac{\frac{\left(4p\right)^{-2}}{q^{-2}}}{\frac{1}{8}q^{3}} as a single fraction.

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

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

$$\frac{4^{-2}p^{-2}}{q^{-2}\times \frac{1}{8}q^{3}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

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

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{\frac{1}{16}p^{-2}}{q^{1}\times \frac{1}{8}}$$

Calculate q to the power of 1 and get q.

$$\frac{\frac{1}{16}p^{-2}}{q\times \frac{1}{8}}$$

Expand

$$\frac{1}{2qp^{2}}$$

Solution Steps

To raise \frac{4p}{q} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(\frac{1}{2}q\right)^{3}.

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

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

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

Express \frac{\frac{\left(4p\right)^{-2}}{q^{-2}}}{\frac{1}{8}q^{3}} as a single fraction.

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

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

$$\frac{4^{-2}p^{-2}}{q^{-2}\times \frac{1}{8}q^{3}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

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

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{\frac{1}{16}p^{-2}}{q^{1}\times \frac{1}{8}}$$

Calculate q to the power of 1 and get q.

$$\frac{\frac{1}{16}p^{-2}}{q\times \frac{1}{8}}$$