Basic Math Examples

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

${(8 a^{3} b^{- 5} c^{- 2})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule

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

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

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

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

Step 2

Multiply

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

$8 a^{3} \frac{1}{b^{5}}$ .

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Step 2.1

Combine

8

$8$ and

\frac{1}{b^{5}}

$\frac{1}{b^{5}}$ .

{(a^{3} \frac{8}{b^{5}} c^{- 2})}^{2}

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

Step 2.2

Combine

a^{3}

$a^{3}$ and

\frac{8}{b^{5}}

$\frac{8}{b^{5}}$ .

{(\frac{a^{3} \cdot 8}{b^{5}} c^{- 2})}^{2}

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

{(\frac{a^{3} \cdot 8}{b^{5}} c^{- 2})}^{2}

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

Step 3

Move

8

$8$ to the left of

a^{3}

$a^{3}$ .

{(\frac{8 \cdot a^{3}}{b^{5}} c^{- 2})}^{2}

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

Step 4

Rewrite the expression using the negative exponent rule

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

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

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

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

Step 5

Combine.

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

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

Step 6

Multiply

8

$8$ by

1

$1$ .

{(\frac{8 a^{3}}{b^{5} c^{2}})}^{2}

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

Step 7

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 7.1

Apply the product rule to

\frac{8 a^{3}}{b^{5} c^{2}}

$\frac{8 a^{3}}{b^{5} c^{2}}$ .

\frac{{(8 a^{3})}^{2}}{{(b^{5} c^{2})}^{2}}

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

Step 7.2

Apply the product rule to

8 a^{3}

$8 a^{3}$ .

\frac{8^{2} {(a^{3})}^{2}}{{(b^{5} c^{2})}^{2}}

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

Step 7.3

Apply the product rule to

b^{5} c^{2}

$b^{5} c^{2}$ .

\frac{8^{2} {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}

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

\frac{8^{2} {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}

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

Step 8

Simplify the numerator.

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Step 8.1

Raise

8

$8$ to the power of

2

$2$ .

\frac{64 {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}

$\frac{64 {(a^{3})}^{2}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 8.2

Multiply the exponents in

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

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

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Step 8.2.1

Apply the power rule and multiply exponents,

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

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

\frac{64 a^{3 \cdot 2}}{{(b^{5})}^{2} {(c^{2})}^{2}}

$\frac{64 a^{3 \cdot 2}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 8.2.2

Multiply

3

$3$ by

2

$2$ .

\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}

$\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}

$\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}

$\frac{64 a^{6}}{{(b^{5})}^{2} {(c^{2})}^{2}}$

Step 9

Simplify the denominator.

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Step 9.1

Multiply the exponents in

{(b^{5})}^{2}

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

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Step 9.1.1

Apply the power rule and multiply exponents,

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

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

\frac{64 a^{6}}{b^{5 \cdot 2} {(c^{2})}^{2}}

$\frac{64 a^{6}}{b^{5 \cdot 2} {(c^{2})}^{2}}$

Step 9.1.2

Multiply

5

$5$ by

2

$2$ .

\frac{64 a^{6}}{b^{10} {(c^{2})}^{2}}

$\frac{64 a^{6}}{b^{10} {(c^{2})}^{2}}$

\frac{64 a^{6}}{b^{10} {(c^{2})}^{2}}

$\frac{64 a^{6}}{b^{10} {(c^{2})}^{2}}$

Step 9.2

Multiply the exponents in

{(c^{2})}^{2}

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

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Step 9.2.1

Apply the power rule and multiply exponents,

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

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

\frac{64 a^{6}}{b^{10} c^{2 \cdot 2}}

$\frac{64 a^{6}}{b^{10} c^{2 \cdot 2}}$

Step 9.2.2

Multiply

2

$2$ by

2

$2$ .

\frac{64 a^{6}}{b^{10} c^{4}}

$\frac{64 a^{6}}{b^{10} c^{4}}$

\frac{64 a^{6}}{b^{10} c^{4}}

$\frac{64 a^{6}}{b^{10} c^{4}}$

\frac{64 a^{6}}{b^{10} c^{4}}

$\frac{64 a^{6}}{b^{10} c^{4}}$