Basic Math Examples

{(5 a^{3} b^{- 2} c^{5})}^{2}

${(5 a^{3} b^{- 2} c^{5})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

{(5 a^{3} \frac{1}{b^{2}} c^{5})}^{2}

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

Step 2

Multiply

5 a^{3} \frac{1}{b^{2}}

$5 a^{3} \frac{1}{b^{2}}$ .

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Step 2.1

Combine

5

$5$ and

\frac{1}{b^{2}}

$\frac{1}{b^{2}}$ .

{(a^{3} \frac{5}{b^{2}} c^{5})}^{2}

${(a^{3} \frac{5}{b^{2}} c^{5})}^{2}$

Step 2.2

Combine

a^{3}

$a^{3}$ and

\frac{5}{b^{2}}

$\frac{5}{b^{2}}$ .

{(\frac{a^{3} \cdot 5}{b^{2}} c^{5})}^{2}

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

{(\frac{a^{3} \cdot 5}{b^{2}} c^{5})}^{2}

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

Step 3

Move

5

$5$ to the left of

a^{3}

$a^{3}$ .

{(\frac{5 \cdot a^{3}}{b^{2}} c^{5})}^{2}

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

Step 4

Combine

$\frac{5 a^{3}}{b^{2}}$ and

$c^{5}$ .

${(\frac{5 a^{3} c^{5}}{b^{2}})}^{2}$

Step 5

Use the power rule

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

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Step 5.1

Apply the product rule to

$\frac{5 a^{3} c^{5}}{b^{2}}$ .

$\frac{{(5 a^{3} c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 5.2

Apply the product rule to

$5 a^{3} c^{5}$ .

$\frac{{(5 a^{3})}^{2} {(c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 5.3

Apply the product rule to

$5 a^{3}$ .

$\frac{5^{2} {(a^{3})}^{2} {(c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Raise

$5$ to the power of

$2$ .

$\frac{25 {(a^{3})}^{2} {(c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 6.2

Multiply the exponents in

${(a^{3})}^{2}$ .

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Step 6.2.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{25 a^{3 \cdot 2} {(c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 6.2.2

Multiply

$3$ by

$2$ .

$\frac{25 a^{6} {(c^{5})}^{2}}{{(b^{2})}^{2}}$

Step 6.3

Multiply the exponents in

${(c^{5})}^{2}$ .

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Step 6.3.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{25 a^{6} c^{5 \cdot 2}}{{(b^{2})}^{2}}$

Step 6.3.2

Multiply

$5$ by

$2$ .

$\frac{25 a^{6} c^{10}}{{(b^{2})}^{2}}$

Step 7

Multiply the exponents in

${(b^{2})}^{2}$ .

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Step 7.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{25 a^{6} c^{10}}{b^{2 \cdot 2}}$

Step 7.2

Multiply

$2$ by

$2$ .

$\frac{25 a^{6} c^{10}}{b^{4}}$