Solve (2r^3/s)(s/r^3)^3

$$( \frac { 2 r ^ { 3 } } { s } ) ( \frac { s } { r ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{2s^{2}}{r^{6}}$$

Solution Steps

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

$$\frac{2r^{3}}{s}\times \frac{s^{3}}{\left(r^{3}\right)^{3}}$$

Multiply \frac{2r^{3}}{s} times \frac{s^{3}}{\left(r^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2r^{3}s^{3}}{s\left(r^{3}\right)^{3}}$$

Cancel out s in both numerator and denominator.

$$\frac{2s^{2}r^{3}}{\left(r^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{2s^{2}r^{3}}{r^{9}}$$

Cancel out r^{3} in both numerator and denominator.

$$\frac{2s^{2}}{r^{6}}$$

Expand

$$\frac{2s^{2}}{r^{6}}$$

Solution Steps

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

$$\frac{2r^{3}}{s}\times \frac{s^{3}}{\left(r^{3}\right)^{3}}$$

Multiply \frac{2r^{3}}{s} times \frac{s^{3}}{\left(r^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2r^{3}s^{3}}{s\left(r^{3}\right)^{3}}$$

Cancel out s in both numerator and denominator.

$$\frac{2s^{2}r^{3}}{\left(r^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{2s^{2}r^{3}}{r^{9}}$$

Cancel out r^{3} in both numerator and denominator.

$$\frac{2s^{2}}{r^{6}}$$