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

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

Evaluate

$$54r^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply 3 and 2 to get 6.

$$\frac{\left(6r^{4}\right)^{3}}{2r^{3}\times 2}$$

Expand \left(6r^{4}\right)^{3}.

$$\frac{6^{3}\left(r^{4}\right)^{3}}{2r^{3}\times 2}$$

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

$$\frac{6^{3}r^{12}}{2r^{3}\times 2}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{216r^{12}}{2r^{3}\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{216r^{12}}{4r^{3}}$$

Cancel out 4r^{3} in both numerator and denominator.

$$54r^{9}$$

Expand

$$54r^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply 3 and 2 to get 6.

$$\frac{\left(6r^{4}\right)^{3}}{2r^{3}\times 2}$$

Expand \left(6r^{4}\right)^{3}.

$$\frac{6^{3}\left(r^{4}\right)^{3}}{2r^{3}\times 2}$$

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

$$\frac{6^{3}r^{12}}{2r^{3}\times 2}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{216r^{12}}{2r^{3}\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{216r^{12}}{4r^{3}}$$

Cancel out 4r^{3} in both numerator and denominator.

$$54r^{9}$$