Pre-Algebra Examples

$\frac{{(x^{\frac{4}{3}})}^{2}}{{(x^{3})}^{\frac{5}{3}}}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Multiply the exponents in ${(x^{\frac{4}{3}})}^{2}$ .

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Step 1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{\frac{4}{3} \cdot 2}}{{(x^{3})}^{\frac{5}{3}}}$

Step 1.1.2

Multiply $\frac{4}{3} \cdot 2$ .

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Step 1.1.2.1

Combine $\frac{4}{3}$ and $2$ .

$\frac{x^{\frac{4 \cdot 2}{3}}}{{(x^{3})}^{\frac{5}{3}}}$

Step 1.1.2.2

Multiply $4$ by $2$ .

$\frac{x^{\frac{8}{3}}}{{(x^{3})}^{\frac{5}{3}}}$

Step 1.2

Multiply the exponents in ${(x^{3})}^{\frac{5}{3}}$ .

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Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{\frac{8}{3}}}{x^{3 (\frac{5}{3})}}$

Step 1.2.2

Cancel the common factor of $3$ .

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Step 1.2.2.1

Cancel the common factor.

$\frac{x^{\frac{8}{3}}}{x^{3 (\frac{5}{3})}}$

Step 1.2.2.2

Rewrite the expression.

$\frac{x^{\frac{8}{3}}}{x^{5}}$

Step 1.3

Move $x^{\frac{8}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{x^{5} x^{- \frac{8}{3}}}$

Step 1.4

Multiply $x^{5}$ by $x^{- \frac{8}{3}}$ by adding the exponents.

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Step 1.4.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{5 - \frac{8}{3}}}$

Step 1.4.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{x^{5 \cdot \frac{3}{3} - \frac{8}{3}}}$

Step 1.4.3

Combine $5$ and $\frac{3}{3}$ .

$\frac{1}{x^{\frac{5 \cdot 3}{3} - \frac{8}{3}}}$

Step 1.4.4

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{5 \cdot 3 - 8}{3}}}$

Step 1.4.5

Simplify the numerator.

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Step 1.4.5.1

Multiply $5$ by $3$ .

$\frac{1}{x^{\frac{15 - 8}{3}}}$

Step 1.4.5.2

Subtract $8$ from $15$ .

$\frac{1}{x^{\frac{7}{3}}}$

Step 2

The degree cannot be determined because $\frac{1}{x^{\frac{7}{3}}}$ is not a polynomial.

Not a polynomial