Basic Math Examples

${(5^{\frac{3}{2}} a^{\frac{9}{8}} b^{- \frac{3}{4}} c^{\frac{1}{8}})}^{\frac{4}{3}}$

Step 1

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

${(5^{\frac{3}{2}} a^{\frac{9}{8}} \frac{1}{b^{\frac{3}{4}}} c^{\frac{1}{8}})}^{\frac{4}{3}}$

Step 2

Multiply $5^{\frac{3}{2}} a^{\frac{9}{8}} \frac{1}{b^{\frac{3}{4}}}$ .

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Step 2.1

Combine $5^{\frac{3}{2}}$ and $\frac{1}{b^{\frac{3}{4}}}$ .

${(a^{\frac{9}{8}} \frac{5^{\frac{3}{2}}}{b^{\frac{3}{4}}} c^{\frac{1}{8}})}^{\frac{4}{3}}$

Step 2.2

Combine $a^{\frac{9}{8}}$ and $\frac{5^{\frac{3}{2}}}{b^{\frac{3}{4}}}$ .

${(\frac{a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}}}{b^{\frac{3}{4}}} c^{\frac{1}{8}})}^{\frac{4}{3}}$

Step 3

Combine $\frac{a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}}}{b^{\frac{3}{4}}}$ and $c^{\frac{1}{8}}$ .

${(\frac{a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}} c^{\frac{1}{8}}}{b^{\frac{3}{4}}})}^{\frac{4}{3}}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}} c^{\frac{1}{8}}}{b^{\frac{3}{4}}}$ .

$\frac{{(a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}} c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 4.2

Apply the product rule to $a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}} c^{\frac{1}{8}}$ .

$\frac{{(a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 4.3

Apply the product rule to $a^{\frac{9}{8}} \cdot 5^{\frac{3}{2}}$ .

$\frac{{(a^{\frac{9}{8}})}^{\frac{4}{3}} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply the exponents in ${(a^{\frac{9}{8}})}^{\frac{4}{3}}$ .

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Step 5.1.1

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

$\frac{a^{\frac{9}{8} \cdot \frac{4}{3}} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.2

Cancel the common factor of $3$ .

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Step 5.1.2.1

Factor $3$ out of $9$ .

$\frac{a^{\frac{3 (3)}{8} \cdot \frac{4}{3}} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.2.2

Cancel the common factor.

$\frac{a^{\frac{3 \cdot 3}{8} \cdot \frac{4}{3}} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.2.3

Rewrite the expression.

$\frac{a^{\frac{3}{8} \cdot 4} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.3

Cancel the common factor of $4$ .

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Step 5.1.3.1

Factor $4$ out of $8$ .

$\frac{a^{\frac{3}{4 (2)} \cdot 4} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.3.2

Cancel the common factor.

$\frac{a^{\frac{3}{4 \cdot 2} \cdot 4} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.1.3.3

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot {(5^{\frac{3}{2}})}^{\frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2

Multiply the exponents in ${(5^{\frac{3}{2}})}^{\frac{4}{3}}$ .

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Step 5.2.1

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

$\frac{a^{\frac{3}{2}} \cdot 5^{\frac{3}{2} \cdot \frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2.2

Cancel the common factor of $3$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{a^{\frac{3}{2}} \cdot 5^{\frac{3}{2} \cdot \frac{4}{3}} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2.2.2

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot 5^{\frac{1}{2} \cdot 4} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2.3

Cancel the common factor of $2$ .

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Step 5.2.3.1

Factor $2$ out of $4$ .

$\frac{a^{\frac{3}{2}} \cdot 5^{\frac{1}{2} \cdot (2 (2))} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2.3.2

Cancel the common factor.

$\frac{a^{\frac{3}{2}} \cdot 5^{\frac{1}{2} \cdot (2 \cdot 2)} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.2.3.3

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot 5^{2} {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.3

Raise $5$ to the power of $2$ .

$\frac{a^{\frac{3}{2}} \cdot 25 {(c^{\frac{1}{8}})}^{\frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4

Multiply the exponents in ${(c^{\frac{1}{8}})}^{\frac{4}{3}}$ .

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Step 5.4.1

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

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{8} \cdot \frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4.2

Cancel the common factor of $4$ .

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Step 5.4.2.1

Factor $4$ out of $8$ .

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{4 (2)} \cdot \frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4.2.2

Cancel the common factor.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{4 \cdot 2} \cdot \frac{4}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4.2.3

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{2} \cdot \frac{1}{3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4.3

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{2 \cdot 3}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 5.4.4

Multiply $2$ by $3$ .

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{{(b^{\frac{3}{4}})}^{\frac{4}{3}}}$

Step 6

Simplify the denominator.

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Step 6.1

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

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Step 6.1.1

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

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b^{\frac{3}{4} \cdot \frac{4}{3}}}$

Step 6.1.2

Cancel the common factor of $3$ .

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Step 6.1.2.1

Cancel the common factor.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b^{\frac{3}{4} \cdot \frac{4}{3}}}$

Step 6.1.2.2

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b^{\frac{1}{4} \cdot 4}}$

Step 6.1.3

Cancel the common factor of $4$ .

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Step 6.1.3.1

Cancel the common factor.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b^{\frac{1}{4} \cdot 4}}$

Step 6.1.3.2

Rewrite the expression.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b^{1}}$

Step 6.2

Simplify.

$\frac{a^{\frac{3}{2}} \cdot 25 c^{\frac{1}{6}}}{b}$

Step 7

Move $25$ to the left of $a^{\frac{3}{2}}$ .

$\frac{25 a^{\frac{3}{2}} c^{\frac{1}{6}}}{b}$