Solve (frac{3s^frac{5{4}}}{2s^-5})^6

$$( \frac { 3 s ^ { \frac { 5 } { 4 } } } { 2 s ^ { - 5 } } ) ^ { 6 }$$

Evaluate

$$\frac{729s^{\frac{75}{2}}}{64}$$

Solution Steps

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

$$\left(\frac{3s^{\frac{25}{4}}}{2}\right)^{6}$$

To raise \frac{3s^{\frac{25}{4}}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3s^{\frac{25}{4}}\right)^{6}}{2^{6}}$$

Expand \left(3s^{\frac{25}{4}}\right)^{6}.

$$\frac{3^{6}\left(s^{\frac{25}{4}}\right)^{6}}{2^{6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{25}{4} and 6 to get \frac{75}{2}.

$$\frac{3^{6}s^{\frac{75}{2}}}{2^{6}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{729s^{\frac{75}{2}}}{2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{729s^{\frac{75}{2}}}{64}$$

Expand

$$\frac{729s^{\frac{75}{2}}}{64}$$

Solution Steps

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

$$\left(\frac{3s^{\frac{25}{4}}}{2}\right)^{6}$$

To raise \frac{3s^{\frac{25}{4}}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3s^{\frac{25}{4}}\right)^{6}}{2^{6}}$$

Expand \left(3s^{\frac{25}{4}}\right)^{6}.

$$\frac{3^{6}\left(s^{\frac{25}{4}}\right)^{6}}{2^{6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{25}{4} and 6 to get \frac{75}{2}.

$$\frac{3^{6}s^{\frac{75}{2}}}{2^{6}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{729s^{\frac{75}{2}}}{2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{729s^{\frac{75}{2}}}{64}$$