Solve frac{(3x^{3}+3x^{3})^2}{3x^3*3x^3*3x^3}

$$\frac { ( 3 x ^ { 3 } + 3 x ^ { 3 } ) ^ { 2 } } { 3 x ^ { 3 } \cdot 3 x ^ { 3 } \cdot 3 x ^ { 3 } }$$

Evaluate

$$\frac{4}{3x^{3}}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\left(3x^{3}+3x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

Combine 3x^{3} and 3x^{3} to get 6x^{3}.

$$\frac{\left(6x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

Expand \left(6x^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{6^{2}x^{6}}{3x^{9}\times 3\times 3}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{6}}{3x^{9}\times 3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{36x^{6}}{9x^{9}\times 3}$$

Multiply 9 and 3 to get 27.

$$\frac{36x^{6}}{27x^{9}}$$

Cancel out 9x^{6} in both numerator and denominator.

$$\frac{4}{3x^{3}}$$

Expand

$$\frac{4}{3x^{3}}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\left(3x^{3}+3x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

Combine 3x^{3} and 3x^{3} to get 6x^{3}.

$$\frac{\left(6x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

Expand \left(6x^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{3}\right)^{2}}{3x^{9}\times 3\times 3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{6^{2}x^{6}}{3x^{9}\times 3\times 3}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{6}}{3x^{9}\times 3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{36x^{6}}{9x^{9}\times 3}$$

Multiply 9 and 3 to get 27.

$$\frac{36x^{6}}{27x^{9}}$$

Cancel out 9x^{6} in both numerator and denominator.

$$\frac{4}{3x^{3}}$$