Algebra Examples

$\frac{{(8 s^{3} t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1

Simplify the numerator.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $8 s^{3} t^{3}$ .

$\frac{{(8 s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.1.2

Apply the product rule to $8 s^{3}$ .

$\frac{8^{\frac{2}{3}} {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.2

Rewrite $8$ as $2^{3}$ .

$\frac{{(2^{3})}^{\frac{2}{3}} {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.3

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

$\frac{2^{3 (\frac{2}{3})} {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Cancel the common factor.

$\frac{2^{3 (\frac{2}{3})} {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.4.2

Rewrite the expression.

$\frac{2^{2} {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.5

Raise $2$ to the power of $2$ .

$\frac{4 {(s^{3})}^{\frac{2}{3}} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.6

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

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Step 1.6.1

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

$\frac{4 s^{3 (\frac{2}{3})} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.6.2

Cancel the common factor of $3$ .

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Step 1.6.2.1

Cancel the common factor.

$\frac{4 s^{3 (\frac{2}{3})} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.6.2.2

Rewrite the expression.

$\frac{4 s^{2} {(t^{3})}^{\frac{2}{3}}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.7

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

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Step 1.7.1

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

$\frac{4 s^{2} t^{3 (\frac{2}{3})}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.7.2

Cancel the common factor of $3$ .

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Step 1.7.2.1

Cancel the common factor.

$\frac{4 s^{2} t^{3 (\frac{2}{3})}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 1.7.2.2

Rewrite the expression.

$\frac{4 s^{2} t^{2}}{{(s^{4} t^{- 8})}^{\frac{1}{4}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 s^{2} t^{2}}{{(s^{4} \frac{1}{t^{8}})}^{\frac{1}{4}}}$

Step 2.2

Combine $s^{4}$ and $\frac{1}{t^{8}}$ .

$\frac{4 s^{2} t^{2}}{{(\frac{s^{4}}{t^{8}})}^{\frac{1}{4}}}$

Step 2.3

Apply the product rule to $\frac{s^{4}}{t^{8}}$ .

$\frac{4 s^{2} t^{2}}{\frac{{(s^{4})}^{\frac{1}{4}}}{{(t^{8})}^{\frac{1}{4}}}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply the exponents in ${(s^{4})}^{\frac{1}{4}}$ .

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Step 2.4.1.1

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

$\frac{4 s^{2} t^{2}}{\frac{s^{4 (\frac{1}{4})}}{{(t^{8})}^{\frac{1}{4}}}}$

Step 2.4.1.2

Cancel the common factor of $4$ .

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Step 2.4.1.2.1

Cancel the common factor.

$\frac{4 s^{2} t^{2}}{\frac{s^{4 (\frac{1}{4})}}{{(t^{8})}^{\frac{1}{4}}}}$

Step 2.4.1.2.2

Rewrite the expression.

$\frac{4 s^{2} t^{2}}{\frac{s^{1}}{{(t^{8})}^{\frac{1}{4}}}}$

Step 2.4.2

Simplify.

$\frac{4 s^{2} t^{2}}{\frac{s}{{(t^{8})}^{\frac{1}{4}}}}$

Step 2.5

Multiply the exponents in ${(t^{8})}^{\frac{1}{4}}$ .

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Step 2.5.1

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

$\frac{4 s^{2} t^{2}}{\frac{s}{t^{8 (\frac{1}{4})}}}$

Step 2.5.2

Cancel the common factor of $4$ .

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Step 2.5.2.1

Factor $4$ out of $8$ .

$\frac{4 s^{2} t^{2}}{\frac{s}{t^{4 (2) \frac{1}{4}}}}$

Step 2.5.2.2

Cancel the common factor.

$\frac{4 s^{2} t^{2}}{\frac{s}{t^{4 \cdot 2 \frac{1}{4}}}}$

Step 2.5.2.3

Rewrite the expression.

$\frac{4 s^{2} t^{2}}{\frac{s}{t^{2}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$4 s^{2} t^{2} \frac{t^{2}}{s}$

Step 4

Cancel the common factor of $s$ .

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Step 4.1

Factor $s$ out of $4 s^{2} t^{2}$ .

$s (4 s t^{2}) \frac{t^{2}}{s}$

Step 4.2

Cancel the common factor.

$s (4 s t^{2}) \frac{t^{2}}{s}$

Step 4.3

Rewrite the expression.

$4 s t^{2} t^{2}$

Step 5

Multiply $t^{2}$ by $t^{2}$ by adding the exponents.

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Step 5.1

Move $t^{2}$ .

$4 s (t^{2} t^{2})$

Step 5.2

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

$4 s t^{2 + 2}$

Step 5.3

Add $2$ and $2$ .

$4 s t^{4}$