Basic Math Examples

{(\frac{2 a^{0} b^{- 2} c^{- 3} \cdot b}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} b^{- 2} c^{- 3} \cdot b}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1

Multiply

b^{- 2}

$b^{- 2}$ by

b

$b$ by adding the exponents.

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Step 1.1

Move

b

$b$ .

{(\frac{2 a^{0} (b \cdot b^{- 2}) c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} (b \cdot b^{- 2}) c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1.2

Multiply

b

$b$ by

b^{- 2}

$b^{- 2}$ .

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Step 1.2.1

Raise

b

$b$ to the power of

1

$1$ .

{(\frac{2 a^{0} (b^{1} b^{- 2}) c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} (b^{1} b^{- 2}) c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{(\frac{2 a^{0} b^{1 - 2} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} b^{1 - 2} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

{(\frac{2 a^{0} b^{1 - 2} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} b^{1 - 2} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 1.3

Subtract

2

$2$ from

1

$1$ .

{(\frac{2 a^{0} b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

{(\frac{2 a^{0} b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

${(\frac{2 a^{0} b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}$

Step 2

Simplify

2 a^{0} b^{- 1} c^{- 3}

$2 a^{0} b^{- 1} c^{- 3}$ .

{(\frac{2 b^{- 1} c^{- 3}}{2 a^{- 3} c^{4}})}^{- 3}

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

Step 3

Move

b^{- 1}

$b^{- 1}$ to the denominator using the negative exponent rule

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

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

{(\frac{2 c^{- 3}}{2 a^{- 3} c^{4} b})}^{- 3}

${(\frac{2 c^{- 3}}{2 a^{- 3} c^{4} b})}^{- 3}$

Step 4

Move

c^{- 3}

$c^{- 3}$ to the denominator using the negative exponent rule

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

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

{(\frac{2}{2 a^{- 3} c^{4} b c^{3}})}^{- 3}

${(\frac{2}{2 a^{- 3} c^{4} b c^{3}})}^{- 3}$

Step 5

Multiply

c^{4}

$c^{4}$ by

c^{3}

$c^{3}$ by adding the exponents.

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Step 5.1

Move

c^{3}

$c^{3}$ .

{(\frac{2}{2 a^{- 3} (c^{3} c^{4}) b})}^{- 3}

${(\frac{2}{2 a^{- 3} (c^{3} c^{4}) b})}^{- 3}$

Step 5.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{(\frac{2}{2 a^{- 3} c^{3 + 4} b})}^{- 3}

${(\frac{2}{2 a^{- 3} c^{3 + 4} b})}^{- 3}$

Step 5.3

Add

3

$3$ and

4

$4$ .

{(\frac{2}{2 a^{- 3} c^{7} b})}^{- 3}

${(\frac{2}{2 a^{- 3} c^{7} b})}^{- 3}$

{(\frac{2}{2 a^{- 3} c^{7} b})}^{- 3}

${(\frac{2}{2 a^{- 3} c^{7} b})}^{- 3}$

Step 6

Move

a^{- 3}

$a^{- 3}$ to the numerator using the negative exponent rule

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

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

{(\frac{2 a^{3}}{2 c^{7} b})}^{- 3}

${(\frac{2 a^{3}}{2 c^{7} b})}^{- 3}$

Step 7

Cancel the common factor of

2

$2$ .

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Step 7.1

Cancel the common factor.

${(\frac{2 a^{3}}{2 c^{7} b})}^{- 3}$

Step 7.2

Rewrite the expression.

${(\frac{a^{3}}{c^{7} b})}^{- 3}$

Step 8

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{c^{7} b}{a^{3}})}^{3}$

Step 9

Use the power rule

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

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Step 9.1

Apply the product rule to

$\frac{c^{7} b}{a^{3}}$ .

$\frac{{(c^{7} b)}^{3}}{{(a^{3})}^{3}}$

Step 9.2

Apply the product rule to

$c^{7} b$ .

$\frac{{(c^{7})}^{3} b^{3}}{{(a^{3})}^{3}}$

Step 10

Multiply the exponents in

${(c^{7})}^{3}$ .

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Step 10.1

Apply the power rule and multiply exponents,

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

$\frac{c^{7 \cdot 3} b^{3}}{{(a^{3})}^{3}}$

Step 10.2

Multiply

$7$ by

$3$ .

$\frac{c^{21} b^{3}}{{(a^{3})}^{3}}$

Step 11

Multiply the exponents in

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

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Step 11.1

Apply the power rule and multiply exponents,

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

$\frac{c^{21} b^{3}}{a^{3 \cdot 3}}$

Step 11.2

Multiply

$3$ by

$3$ .

$\frac{c^{21} b^{3}}{a^{9}}$