Solve (frac{3p^{4}q^{-1}}{8p^{-2}q^3})^-2*(q^-2/4p^-1)

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

Evaluate

$$\frac{16q^{6}}{9p^{11}}$$

Solution Steps

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

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

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

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

To raise \frac{3p^{6}}{8q^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(3p^{6}\right)^{-2}}{\left(8q^{4}\right)^{-2}} times \frac{q^{-2}}{4p^{-1}} by multiplying numerator times numerator and denominator times denominator.

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

Expand \left(3p^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{3^{-2}p^{-12}q^{-2}}{\left(8q^{4}\right)^{-2}\times 4p^{-1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\left(8q^{4}\right)^{-2}\times 4p^{-1}}$$

Expand \left(8q^{4}\right)^{-2}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{8^{-2}\left(q^{4}\right)^{-2}\times 4p^{-1}}$$

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

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{8^{-2}q^{-8}\times 4p^{-1}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\frac{1}{64}q^{-8}\times 4p^{-1}}$$

Multiply \frac{1}{64} and 4 to get \frac{1}{16}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\frac{1}{16}q^{-8}p^{-1}}$$

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

$$\frac{\frac{1}{9}p^{-12}q^{6}}{\frac{1}{16}\times \frac{1}{p}}$$

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

$$\frac{\frac{1}{9}q^{6}}{\frac{1}{16}p^{11}}$$

Expand

$$\frac{16q^{6}}{9p^{11}}$$

Solution Steps

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

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

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

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

To raise \frac{3p^{6}}{8q^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(3p^{6}\right)^{-2}}{\left(8q^{4}\right)^{-2}} times \frac{q^{-2}}{4p^{-1}} by multiplying numerator times numerator and denominator times denominator.

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

Expand \left(3p^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{3^{-2}p^{-12}q^{-2}}{\left(8q^{4}\right)^{-2}\times 4p^{-1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\left(8q^{4}\right)^{-2}\times 4p^{-1}}$$

Expand \left(8q^{4}\right)^{-2}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{8^{-2}\left(q^{4}\right)^{-2}\times 4p^{-1}}$$

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

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{8^{-2}q^{-8}\times 4p^{-1}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\frac{1}{64}q^{-8}\times 4p^{-1}}$$

Multiply \frac{1}{64} and 4 to get \frac{1}{16}.

$$\frac{\frac{1}{9}p^{-12}q^{-2}}{\frac{1}{16}q^{-8}p^{-1}}$$

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

$$\frac{\frac{1}{9}p^{-12}q^{6}}{\frac{1}{16}\times \frac{1}{p}}$$

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

$$\frac{\frac{1}{9}q^{6}}{\frac{1}{16}p^{11}}$$