Solve (2r^3/5)(5/r^3)^3

$$( \frac { 2 r ^ { 3 } } { 5 } ) ( \frac { 5 } { r ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{50}{r^{6}}$$

Solution Steps

To raise \frac{5}{r^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2r^{3}}{5}\times \frac{5^{3}}{\left(r^{3}\right)^{3}}$$

Multiply \frac{2r^{3}}{5} times \frac{5^{3}}{\left(r^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2r^{3}\times 5^{3}}{5\left(r^{3}\right)^{3}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\times 5^{2}r^{3}}{\left(r^{3}\right)^{3}}$$

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

$$\frac{2\times 5^{2}r^{3}}{r^{9}}$$

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

$$\frac{2\times 5^{2}}{r^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2\times 25}{r^{6}}$$

Multiply 2 and 25 to get 50.

$$\frac{50}{r^{6}}$$

Expand

$$\frac{50}{r^{6}}$$

Solution Steps

To raise \frac{5}{r^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2r^{3}}{5}\times \frac{5^{3}}{\left(r^{3}\right)^{3}}$$

Multiply \frac{2r^{3}}{5} times \frac{5^{3}}{\left(r^{3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2r^{3}\times 5^{3}}{5\left(r^{3}\right)^{3}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\times 5^{2}r^{3}}{\left(r^{3}\right)^{3}}$$

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

$$\frac{2\times 5^{2}r^{3}}{r^{9}}$$

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

$$\frac{2\times 5^{2}}{r^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2\times 25}{r^{6}}$$

Multiply 2 and 25 to get 50.

$$\frac{50}{r^{6}}$$