Solve (frac{7s^-frac{4{3}}}{6s})^3

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

Evaluate

$$\frac{343}{216s^{7}}$$

Solution Steps

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

$$\left(\frac{7}{6s^{\frac{7}{3}}}\right)^{3}$$

To raise \frac{7}{6s^{\frac{7}{3}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{3}}{\left(6s^{\frac{7}{3}}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{343}{\left(6s^{\frac{7}{3}}\right)^{3}}$$

Expand \left(6s^{\frac{7}{3}}\right)^{3}.

$$\frac{343}{6^{3}\left(s^{\frac{7}{3}}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and 3 to get 7.

$$\frac{343}{6^{3}s^{7}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{343}{216s^{7}}$$

Expand

$$\frac{343}{216s^{7}}$$

Solution Steps

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

$$\left(\frac{7}{6s^{\frac{7}{3}}}\right)^{3}$$

To raise \frac{7}{6s^{\frac{7}{3}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{3}}{\left(6s^{\frac{7}{3}}\right)^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{343}{\left(6s^{\frac{7}{3}}\right)^{3}}$$

Expand \left(6s^{\frac{7}{3}}\right)^{3}.

$$\frac{343}{6^{3}\left(s^{\frac{7}{3}}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and 3 to get 7.

$$\frac{343}{6^{3}s^{7}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{343}{216s^{7}}$$