Solve (q^-1r^3/qr^-2)^-6

$$( \frac { q ^ { - 1 } r ^ { 3 } } { q r ^ { - 2 } } ) ^ { - 6 }$$

Evaluate

$$\frac{q^{12}}{r^{30}}$$

Solution Steps

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

$$\left(\frac{\frac{1}{q}r^{5}}{q}\right)^{-6}$$

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

$$\left(\frac{r^{5}}{q^{2}}\right)^{-6}$$

To raise \frac{r^{5}}{q^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(r^{5}\right)^{-6}}{\left(q^{2}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -6 to get -30.

$$\frac{r^{-30}}{\left(q^{2}\right)^{-6}}$$

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

$$\frac{r^{-30}}{q^{-12}}$$

Expand

$$\frac{q^{12}}{r^{30}}$$

Solution Steps

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

$$\left(\frac{\frac{1}{q}r^{5}}{q}\right)^{-6}$$

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

$$\left(\frac{r^{5}}{q^{2}}\right)^{-6}$$

To raise \frac{r^{5}}{q^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(r^{5}\right)^{-6}}{\left(q^{2}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -6 to get -30.

$$\frac{r^{-30}}{\left(q^{2}\right)^{-6}}$$

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

$$\frac{r^{-30}}{q^{-12}}$$