Solve (frac{p^{2}}{3q})^3*(p^2/q^3)^-2

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

Evaluate

$$\frac{p^{2}q^{3}}{27}$$

Solution Steps

To raise \frac{p^{2}}{3q} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{p^{2}}{q^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{p^{2}}{3^{3}q^{3}q^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{p^{2}}{27q^{3}q^{-6}}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$\frac{p^{2}}{27q^{-3}}$$

Expand

$$\frac{p^{2}q^{3}}{27}$$

Solution Steps

To raise \frac{p^{2}}{3q} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{p^{2}}{q^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{p^{2}}{3^{3}q^{3}q^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{p^{2}}{27q^{3}q^{-6}}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$\frac{p^{2}}{27q^{-3}}$$