Algebra Examples

$(36 a^{4} b^{0} c^{48}) (2 a^{0} b^{- 6} c^{- 28})$

Step 1

Multiply $a^{4}$ by $a^{0}$ by adding the exponents.

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Step 1.1

Move $a^{0}$ .

$36 (a^{0} a^{4}) b^{0} c^{48} (2 b^{- 6} c^{- 28})$

Step 1.2

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

$36 a^{0 + 4} b^{0} c^{48} (2 b^{- 6} c^{- 28})$

Step 1.3

Add $0$ and $4$ .

$36 a^{4} b^{0} c^{48} (2 b^{- 6} c^{- 28})$

Step 2

Simplify $36 a^{4} b^{0} c^{48} (2 b^{- 6} c^{- 28})$ .

$36 a^{4} c^{48} (2 b^{- 6} c^{- 28})$

Step 3

Multiply $c^{48}$ by $c^{- 28}$ by adding the exponents.

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Step 3.1

Move $c^{- 28}$ .

$36 a^{4} (c^{- 28} c^{48}) (2 b^{- 6})$

Step 3.2

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

$36 a^{4} c^{- 28 + 48} (2 b^{- 6})$

Step 3.3

Add $- 28$ and $48$ .

$36 a^{4} c^{20} (2 b^{- 6})$

Step 4

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

$36 a^{4} c^{20} (2 \frac{1}{b^{6}})$

Step 5

Combine $2$ and $\frac{1}{b^{6}}$ .

$36 a^{4} c^{20} \frac{2}{b^{6}}$

Step 6

Multiply $36 a^{4} c^{20} \frac{2}{b^{6}}$ .

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Step 6.1

Combine $36$ and $\frac{2}{b^{6}}$ .

$a^{4} c^{20} \frac{36 \cdot 2}{b^{6}}$

Step 6.2

Multiply $36$ by $2$ .

$a^{4} c^{20} \frac{72}{b^{6}}$

Step 6.3

Combine $a^{4}$ and $\frac{72}{b^{6}}$ .

$c^{20} \frac{a^{4} \cdot 72}{b^{6}}$

Step 6.4

Combine $c^{20}$ and $\frac{a^{4} \cdot 72}{b^{6}}$ .

$\frac{c^{20} (a^{4} \cdot 72)}{b^{6}}$

Step 7

Move $72$ to the left of $c^{20} a^{4}$ .

$\frac{72 c^{20} a^{4}}{b^{6}}$