Solve (5^{frac{2/3}3^{-1/2}6^-2}{3^-frac{1{2}}b^-1})^-3

$$( \frac { 5 ^ { \frac { 2 } { 3 } } 3 ^ { - \frac { 1 } { 2 } } 6 ^ { - 2 } } { 3 ^ { - \frac { 1 } { 2 } } b ^ { - 1 } } ) ^ { - 3 }$$

Evaluate

$$\frac{46656}{25b^{3}}$$

Solution Steps

Cancel out 3^{-\frac{1}{2}} in both numerator and denominator.

$$\left(\frac{5^{\frac{2}{3}}\times 6^{-2}}{\frac{1}{b}}\right)^{-3}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\left(\frac{5^{\frac{2}{3}}\times \frac{1}{36}}{\frac{1}{b}}\right)^{-3}$$

To raise \frac{5^{\frac{2}{3}}\times \frac{1}{36}}{\frac{1}{b}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5^{\frac{2}{3}}\times \frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Expand \left(5^{\frac{2}{3}}\times \frac{1}{36}\right)^{-3}.

$$\frac{\left(5^{\frac{2}{3}}\right)^{-3}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

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

$$\frac{5^{-2}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Calculate \frac{1}{36} to the power of -3 and get 46656.

$$\frac{\frac{1}{25}\times 46656}{\left(\frac{1}{b}\right)^{-3}}$$

Multiply \frac{1}{25} and 46656 to get \frac{46656}{25}.

$$\frac{\frac{46656}{25}}{\left(\frac{1}{b}\right)^{-3}}$$

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{46656}{25}}{\frac{1^{-3}}{b^{-3}}}$$

Divide \frac{46656}{25} by \frac{1^{-3}}{b^{-3}} by multiplying \frac{46656}{25} by the reciprocal of \frac{1^{-3}}{b^{-3}}.

$$\frac{46656b^{-3}}{25\times 1^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{46656b^{-3}}{25\times 1}$$

Multiply 25 and 1 to get 25.

$$\frac{46656b^{-3}}{25}$$

Expand

$$\frac{46656}{25b^{3}}$$

Solution Steps

Cancel out 3^{-\frac{1}{2}} in both numerator and denominator.

$$\left(\frac{5^{\frac{2}{3}}\times 6^{-2}}{\frac{1}{b}}\right)^{-3}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\left(\frac{5^{\frac{2}{3}}\times \frac{1}{36}}{\frac{1}{b}}\right)^{-3}$$

To raise \frac{5^{\frac{2}{3}}\times \frac{1}{36}}{\frac{1}{b}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5^{\frac{2}{3}}\times \frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Expand \left(5^{\frac{2}{3}}\times \frac{1}{36}\right)^{-3}.

$$\frac{\left(5^{\frac{2}{3}}\right)^{-3}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

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

$$\frac{5^{-2}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}\times \left(\frac{1}{36}\right)^{-3}}{\left(\frac{1}{b}\right)^{-3}}$$

Calculate \frac{1}{36} to the power of -3 and get 46656.

$$\frac{\frac{1}{25}\times 46656}{\left(\frac{1}{b}\right)^{-3}}$$

Multiply \frac{1}{25} and 46656 to get \frac{46656}{25}.

$$\frac{\frac{46656}{25}}{\left(\frac{1}{b}\right)^{-3}}$$

To raise \frac{1}{b} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{46656}{25}}{\frac{1^{-3}}{b^{-3}}}$$

Divide \frac{46656}{25} by \frac{1^{-3}}{b^{-3}} by multiplying \frac{46656}{25} by the reciprocal of \frac{1^{-3}}{b^{-3}}.

$$\frac{46656b^{-3}}{25\times 1^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{46656b^{-3}}{25\times 1}$$

Multiply 25 and 1 to get 25.

$$\frac{46656b^{-3}}{25}$$