Solve [(1/p^{2})^{3}*(frac{q^{3}}{1})^{2}]*(p^2/q^2)^2div(q/p)^2]

$$[ ( \frac { 1 } { p ^ { 2 } } ) ^ { 3 } \times ( \frac { q ^ { 3 } } { 1 } ) ^ { 2 } ] \times ( \frac { p ^ { 2 } } { q ^ { 2 } } ) ^ { 2 } \div ( \frac { q } { p } ) ^ { 2 } ]$$

Evaluate

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Solution Steps

To raise \frac{1}{p^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Anything divided by one gives itself.

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

To raise \frac{p^{2}}{q^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Multiply \frac{1^{3}\left(q^{3}\right)^{2}}{\left(p^{2}\right)^{3}} times \frac{\left(p^{2}\right)^{2}}{\left(q^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out \left(p^{2}\right)^{2} in both numerator and denominator.

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

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

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

Divide \frac{1^{3}\left(q^{3}\right)^{2}}{p^{2}\left(q^{2}\right)^{2}} by \frac{q^{2}}{p^{2}} by multiplying \frac{1^{3}\left(q^{3}\right)^{2}}{p^{2}\left(q^{2}\right)^{2}} by the reciprocal of \frac{q^{2}}{p^{2}}.

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

Cancel out p^{2} in both numerator and denominator.

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

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

$$\frac{1^{3}q^{6}}{q^{2}\left(q^{2}\right)^{2}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1q^{6}}{q^{2}\left(q^{2}\right)^{2}}$$

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

$$\frac{1q^{6}}{q^{2}q^{4}}$$

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

$$\frac{1q^{6}}{q^{6}}$$

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

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Factor

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