Solve (4A^-6/-8b^3)^4

$$( \frac { 4 A ^ { - 6 } } { - 8 b ^ { 3 } } ) ^ { 4 }$$

Evaluate

$$\frac{1}{16b^{12}A^{24}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

To raise \frac{A^{-6}}{-2b^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$\frac{A^{-24}}{\left(-2b^{3}\right)^{4}}$$

Expand \left(-2b^{3}\right)^{4}.

$$\frac{A^{-24}}{\left(-2\right)^{4}\left(b^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{A^{-24}}{\left(-2\right)^{4}b^{12}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{A^{-24}}{16b^{12}}$$

Expand

$$\frac{1}{16b^{12}A^{24}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

To raise \frac{A^{-6}}{-2b^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$\frac{A^{-24}}{\left(-2b^{3}\right)^{4}}$$

Expand \left(-2b^{3}\right)^{4}.

$$\frac{A^{-24}}{\left(-2\right)^{4}\left(b^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{A^{-24}}{\left(-2\right)^{4}b^{12}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{A^{-24}}{16b^{12}}$$