Solve (frac{-24a^{2}b^9}{8a^7b^-6})^3

$$( \frac { - 24 a ^ { 2 } b ^ { 9 } } { 8 a ^ { 7 } b ^ { - 6 } } ) ^ { 3 }$$

Evaluate

$$-\frac{27b^{45}}{a^{15}}$$

Solution Steps

Cancel out 8a^{2} in both numerator and denominator.

$$\left(\frac{-3b^{9}}{b^{-6}a^{5}}\right)^{3}$$

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

$$\left(\frac{-3b^{15}}{a^{5}}\right)^{3}$$

To raise \frac{-3b^{15}}{a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3b^{15}\right)^{3}}{\left(a^{5}\right)^{3}}$$

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

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

Expand \left(-3b^{15}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$\frac{\left(-3\right)^{3}b^{45}}{a^{15}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27b^{45}}{a^{15}}$$

Expand

$$-\frac{27b^{45}}{a^{15}}$$

Solution Steps

Cancel out 8a^{2} in both numerator and denominator.

$$\left(\frac{-3b^{9}}{b^{-6}a^{5}}\right)^{3}$$

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

$$\left(\frac{-3b^{15}}{a^{5}}\right)^{3}$$

To raise \frac{-3b^{15}}{a^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3b^{15}\right)^{3}}{\left(a^{5}\right)^{3}}$$

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

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

Expand \left(-3b^{15}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$\frac{\left(-3\right)^{3}b^{45}}{a^{15}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27b^{45}}{a^{15}}$$