Solve (frac{-16a^{5}b^3}{8a^8b^-6})^3

$$( \frac { - 16 a ^ { 5 } b ^ { 3 } } { 8 a ^ { 8 } b ^ { - 6 } } ) ^ { 3 }$$

Evaluate

$$-\frac{8b^{27}}{a^{9}}$$

Solution Steps

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

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

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

$$\left(\frac{-2b^{9}}{a^{3}}\right)^{3}$$

To raise \frac{-2b^{9}}{a^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2b^{9}\right)^{3}}{\left(a^{3}\right)^{3}}$$

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

$$\frac{\left(-2b^{9}\right)^{3}}{a^{9}}$$

Expand \left(-2b^{9}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(b^{9}\right)^{3}}{a^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{\left(-2\right)^{3}b^{27}}{a^{9}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8b^{27}}{a^{9}}$$

Expand

$$-\frac{8b^{27}}{a^{9}}$$

Solution Steps

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

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

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

$$\left(\frac{-2b^{9}}{a^{3}}\right)^{3}$$

To raise \frac{-2b^{9}}{a^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2b^{9}\right)^{3}}{\left(a^{3}\right)^{3}}$$

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

$$\frac{\left(-2b^{9}\right)^{3}}{a^{9}}$$

Expand \left(-2b^{9}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(b^{9}\right)^{3}}{a^{9}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{\left(-2\right)^{3}b^{27}}{a^{9}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8b^{27}}{a^{9}}$$