Solve (2w/3w^frac{7{4}})^-6

$$( \frac { 2 w } { 3 w ^ { \frac { 7 } { 4 } } } ) ^ { - 6 }$$

Evaluate

$$\frac{729w^{\frac{9}{2}}}{64}$$

Solution Steps

Cancel out w in both numerator and denominator.

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

To raise \frac{2}{3w^{\frac{3}{4}}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{\frac{1}{64}}{\left(3w^{\frac{3}{4}}\right)^{-6}}$$

Expand \left(3w^{\frac{3}{4}}\right)^{-6}.

$$\frac{\frac{1}{64}}{3^{-6}\left(w^{\frac{3}{4}}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -6 to get -\frac{9}{2}.

$$\frac{\frac{1}{64}}{3^{-6}w^{-\frac{9}{2}}}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{\frac{1}{64}}{\frac{1}{729}w^{-\frac{9}{2}}}$$

Express \frac{\frac{1}{64}}{\frac{1}{729}w^{-\frac{9}{2}}} as a single fraction.

$$\frac{1}{64\times \frac{1}{729}w^{-\frac{9}{2}}}$$

Multiply 64 and \frac{1}{729} to get \frac{64}{729}.

$$\frac{1}{\frac{64}{729}w^{-\frac{9}{2}}}$$

Expand

$$\frac{729w^{\frac{9}{2}}}{64}$$

Solution Steps

Cancel out w in both numerator and denominator.

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

To raise \frac{2}{3w^{\frac{3}{4}}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{\frac{1}{64}}{\left(3w^{\frac{3}{4}}\right)^{-6}}$$

Expand \left(3w^{\frac{3}{4}}\right)^{-6}.

$$\frac{\frac{1}{64}}{3^{-6}\left(w^{\frac{3}{4}}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -6 to get -\frac{9}{2}.

$$\frac{\frac{1}{64}}{3^{-6}w^{-\frac{9}{2}}}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{\frac{1}{64}}{\frac{1}{729}w^{-\frac{9}{2}}}$$

Express \frac{\frac{1}{64}}{\frac{1}{729}w^{-\frac{9}{2}}} as a single fraction.

$$\frac{1}{64\times \frac{1}{729}w^{-\frac{9}{2}}}$$

Multiply 64 and \frac{1}{729} to get \frac{64}{729}.

$$\frac{1}{\frac{64}{729}w^{-\frac{9}{2}}}$$