Algebra Examples

$\frac{4.5 \cdot 10^{- 3} \cdot 2 \cdot 10^{4}}{3.6 \cdot 10^{5} \cdot 2.5 \cdot 10^{- 2}}$

Step 1

Multiply $4.5$ by $2$ .

$\frac{9 (10^{- 3} \cdot 10^{4})}{3.6 \cdot 10^{5} \cdot 2.5 \cdot 10^{- 2}}$

Step 2

Multiply $10^{- 3}$ by $10^{4}$ by adding the exponents.

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Step 2.1

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

$\frac{9 \cdot 10^{- 3 + 4}}{3.6 \cdot 10^{5} \cdot 2.5 \cdot 10^{- 2}}$

Step 2.2

Add $- 3$ and $4$ .

$\frac{9 \cdot 10^{1}}{3.6 \cdot 10^{5} \cdot 2.5 \cdot 10^{- 2}}$

Step 3

Simplify $10^{1}$ .

$\frac{9 \cdot 10}{3.6 \cdot 10^{5} \cdot 2.5 \cdot 10^{- 2}}$

Step 4

Multiply $3.6$ by $2.5$ .

$\frac{9 \cdot 10}{9 (10^{5} \cdot 10^{- 2})}$

Step 5

Multiply $10^{5}$ by $10^{- 2}$ by adding the exponents.

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Step 5.1

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

$\frac{9 \cdot 10}{9 \cdot 10^{5 - 2}}$

Step 5.2

Subtract $2$ from $5$ .

$\frac{9 \cdot 10}{9 \cdot 10^{3}}$

Step 6

Cancel the common factor of $9$ and $9$ .

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Step 6.1

Cancel the common factor.

$\frac{9 \cdot 10}{9 \cdot 10^{3}}$

Step 6.2

Rewrite the expression.

$\frac{10}{10^{3}}$

Step 7

Cancel the common factor of $10$ and $10^{3}$ .

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Step 7.1

Factor $10$ out of $10$ .

$\frac{10 (1)}{10^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $10$ out of $10^{3}$ .

$\frac{10 (1)}{10 \cdot 10^{2}}$

Step 7.2.2

Cancel the common factor.

$\frac{10 \cdot 1}{10 \cdot 10^{2}}$

Step 7.2.3

Rewrite the expression.

$\frac{1}{10^{2}}$

Step 8

Raise $10$ to the power of $2$ .

$\frac{1}{100}$