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

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

Evaluate

$$\frac{27r^{12}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(\frac{r^{6}\times 3}{2r^{2}}\right)^{3}$$

Cancel out r^{2} in both numerator and denominator.

$$\left(\frac{3r^{4}}{2}\right)^{3}$$

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

$$\frac{\left(3r^{4}\right)^{3}}{2^{3}}$$

Expand \left(3r^{4}\right)^{3}.

$$\frac{3^{3}\left(r^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3^{3}r^{12}}{2^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27r^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{27r^{12}}{8}$$

Expand

$$\frac{27r^{12}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(\frac{r^{6}\times 3}{2r^{2}}\right)^{3}$$

Cancel out r^{2} in both numerator and denominator.

$$\left(\frac{3r^{4}}{2}\right)^{3}$$

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

$$\frac{\left(3r^{4}\right)^{3}}{2^{3}}$$

Expand \left(3r^{4}\right)^{3}.

$$\frac{3^{3}\left(r^{4}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3^{3}r^{12}}{2^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27r^{12}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{27r^{12}}{8}$$