Algebra Examples

$\frac{10^{3} \cdot 10^{- 5} \cdot 10^{10}}{10^{6}}$

Step 1

Multiply $10^{3}$ by $10^{- 5}$ by adding the exponents.

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Step 1.1

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

$\frac{10^{3 - 5} \cdot 10^{10}}{10^{6}}$

Step 1.2

Subtract $5$ from $3$ .

$\frac{10^{- 2} \cdot 10^{10}}{10^{6}}$

Step 2

Multiply $10^{- 2}$ by $10^{10}$ 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.

$\frac{10^{- 2 + 10}}{10^{6}}$

Step 2.2

Add $- 2$ and $10$ .

$\frac{10^{8}}{10^{6}}$

Step 3

Cancel the common factor of $10^{8}$ and $10^{6}$ .

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Step 3.1

Factor $10^{6}$ out of $10^{8}$ .

$\frac{10^{6} \cdot 10^{2}}{10^{6}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{10^{6} \cdot 10^{2}}{10^{6} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{10^{6} \cdot 10^{2}}{10^{6} \cdot 1}$

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $10^{2}$ by $1$ .

$10^{2}$

Step 4

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

$100$