Solve (frac{a^{-4}b^2}{a^2b^-3})^3

$$( \frac { a ^ { - 4 } b ^ { 2 } } { a ^ { 2 } b ^ { - 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{b^{15}}{a^{18}}$$

Solution Steps

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

$$\left(\frac{a^{-4}b^{5}}{a^{2}}\right)^{3}$$

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

$$\left(\frac{b^{5}}{a^{6}}\right)^{3}$$

To raise \frac{b^{5}}{a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{5}\right)^{3}}{\left(a^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{b^{15}}{\left(a^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{b^{15}}{a^{18}}$$

Expand

$$\frac{b^{15}}{a^{18}}$$

Solution Steps

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

$$\left(\frac{a^{-4}b^{5}}{a^{2}}\right)^{3}$$

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

$$\left(\frac{b^{5}}{a^{6}}\right)^{3}$$

To raise \frac{b^{5}}{a^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(b^{5}\right)^{3}}{\left(a^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{b^{15}}{\left(a^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{b^{15}}{a^{18}}$$