Solve (x^3)1/2*(x^4)1/2*{left(xfrac{1/3right)}^5}{(x)*(x^11)1/2*(x^3)frac{1}{3}}*4

$$\frac{ ( { x }^{ 3 } ) \frac{ 1 }{ 2 } \times ( { x }^{ 4 } ) \frac{ 1 }{ 2 } \times { \left(x \frac{ 1 }{ 3 } \right) }^{ 5 } }{ (x) \times ( { x }^{ 11 } ) \frac{ 1 }{ 2 } \times ( { x }^{ 3 } ) \frac{ 1 }{ 3 } } \times 4$$

Evaluate

$$\frac{2}{81x^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{xx^{11}\times \frac{1}{2}x^{3}\times \frac{1}{3}}\times 4$$

To multiply powers of the same base, add their exponents. Add 1 and 11 to get 12.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{x^{12}\times \frac{1}{2}x^{3}\times \frac{1}{3}}\times 4$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{x^{15}\times \frac{1}{2}\times \frac{1}{3}}\times 4$$

Cancel out x^{7} in both numerator and denominator.

$$\frac{\frac{1}{2}\times \frac{1}{2}\times \left(\frac{1}{3}x\right)^{5}}{\frac{1}{3}\times \frac{1}{2}x^{8}}\times 4$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(\frac{1}{3}x\right)^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Expand \left(\frac{1}{3}x\right)^{5}.

$$\frac{\left(\frac{1}{3}\right)^{5}x^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times 1\times 2x^{8}}\times 4$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times 2x^{8}}\times 4$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{\frac{1}{243}x^{5}}{\frac{2}{3}x^{8}}\times 4$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{\frac{1}{243}}{\frac{2}{3}x^{3}}\times 4$$

Express \frac{\frac{1}{243}}{\frac{2}{3}x^{3}} as a single fraction.

$$\frac{1}{243\times \frac{2}{3}x^{3}}\times 4$$

Multiply 243 and \frac{2}{3} to get 162.

$$\frac{1}{162x^{3}}\times 4$$

Express \frac{1}{162x^{3}}\times 4 as a single fraction.

$$\frac{4}{162x^{3}}$$

Expand

$$\frac{2}{81x^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{xx^{11}\times \frac{1}{2}x^{3}\times \frac{1}{3}}\times 4$$

To multiply powers of the same base, add their exponents. Add 1 and 11 to get 12.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{x^{12}\times \frac{1}{2}x^{3}\times \frac{1}{3}}\times 4$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$\frac{x^{7}\times \frac{1}{2}\times \frac{1}{2}\left(x\times \frac{1}{3}\right)^{5}}{x^{15}\times \frac{1}{2}\times \frac{1}{3}}\times 4$$

Cancel out x^{7} in both numerator and denominator.

$$\frac{\frac{1}{2}\times \frac{1}{2}\times \left(\frac{1}{3}x\right)^{5}}{\frac{1}{3}\times \frac{1}{2}x^{8}}\times 4$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(\frac{1}{3}x\right)^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Expand \left(\frac{1}{3}x\right)^{5}.

$$\frac{\left(\frac{1}{3}\right)^{5}x^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times \frac{1}{\frac{1}{2}}x^{8}}\times 4$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times 1\times 2x^{8}}\times 4$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{1}{243}x^{5}}{\frac{1}{3}\times 2x^{8}}\times 4$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{\frac{1}{243}x^{5}}{\frac{2}{3}x^{8}}\times 4$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{\frac{1}{243}}{\frac{2}{3}x^{3}}\times 4$$

Express \frac{\frac{1}{243}}{\frac{2}{3}x^{3}} as a single fraction.

$$\frac{1}{243\times \frac{2}{3}x^{3}}\times 4$$

Multiply 243 and \frac{2}{3} to get 162.

$$\frac{1}{162x^{3}}\times 4$$

Express \frac{1}{162x^{3}}\times 4 as a single fraction.

$$\frac{4}{162x^{3}}$$