Solve (4a/b)^-4div(1/2b)^5

$$( \frac { 4 a } { b } ) ^ { - 4 } \div ( \frac { 1 } { 2 } b ) ^ { 5 }$$

Evaluate

$$\frac{1}{8ba^{4}}$$

Solution Steps

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

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\left(\frac{1}{2}b\right)^{5}}$$

Expand \left(\frac{1}{2}b\right)^{5}.

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\left(\frac{1}{2}\right)^{5}b^{5}}$$

Calculate \frac{1}{2} to the power of 5 and get \frac{1}{32}.

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\frac{1}{32}b^{5}}$$

Express \frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\frac{1}{32}b^{5}} as a single fraction.

$$\frac{\left(4a\right)^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

Expand \left(4a\right)^{-4}.

$$\frac{4^{-4}a^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{\frac{1}{256}a^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

To multiply powers of the same base, add their exponents. Add -4 and 5 to get 1.

$$\frac{\frac{1}{256}a^{-4}}{b^{1}\times \frac{1}{32}}$$

Calculate b to the power of 1 and get b.

$$\frac{\frac{1}{256}a^{-4}}{b\times \frac{1}{32}}$$

Expand

$$\frac{1}{8ba^{4}}$$

Solution Steps

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

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\left(\frac{1}{2}b\right)^{5}}$$

Expand \left(\frac{1}{2}b\right)^{5}.

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\left(\frac{1}{2}\right)^{5}b^{5}}$$

Calculate \frac{1}{2} to the power of 5 and get \frac{1}{32}.

$$\frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\frac{1}{32}b^{5}}$$

Express \frac{\frac{\left(4a\right)^{-4}}{b^{-4}}}{\frac{1}{32}b^{5}} as a single fraction.

$$\frac{\left(4a\right)^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

Expand \left(4a\right)^{-4}.

$$\frac{4^{-4}a^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{\frac{1}{256}a^{-4}}{b^{-4}\times \frac{1}{32}b^{5}}$$

To multiply powers of the same base, add their exponents. Add -4 and 5 to get 1.

$$\frac{\frac{1}{256}a^{-4}}{b^{1}\times \frac{1}{32}}$$

Calculate b to the power of 1 and get b.

$$\frac{\frac{1}{256}a^{-4}}{b\times \frac{1}{32}}$$