Solve (frac{-32a^{5}b^6}{8a^8b^-2})^3

$$( \frac { - 32 a ^ { 5 } b ^ { 6 } } { 8 a ^ { 8 } b ^ { - 2 } } ) ^ { 3 }$$

Evaluate

$$-\frac{64b^{24}}{a^{9}}$$

Solution Steps

Cancel out 8a^{5} in both numerator and denominator.

$$\left(\frac{-4b^{6}}{b^{-2}a^{3}}\right)^{3}$$

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

$$\left(\frac{-4b^{8}}{a^{3}}\right)^{3}$$

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

$$\frac{\left(-4b^{8}\right)^{3}}{\left(a^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-4b^{8}\right)^{3}}{a^{9}}$$

Expand \left(-4b^{8}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(b^{8}\right)^{3}}{a^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{\left(-4\right)^{3}b^{24}}{a^{9}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64b^{24}}{a^{9}}$$

Expand

$$-\frac{64b^{24}}{a^{9}}$$

Solution Steps

Cancel out 8a^{5} in both numerator and denominator.

$$\left(\frac{-4b^{6}}{b^{-2}a^{3}}\right)^{3}$$

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

$$\left(\frac{-4b^{8}}{a^{3}}\right)^{3}$$

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

$$\frac{\left(-4b^{8}\right)^{3}}{\left(a^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-4b^{8}\right)^{3}}{a^{9}}$$

Expand \left(-4b^{8}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(b^{8}\right)^{3}}{a^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{\left(-4\right)^{3}b^{24}}{a^{9}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64b^{24}}{a^{9}}$$