Basic Math Examples

${(\frac{1}{10})}^{2} \cdot \frac{1}{10} \cdot {(\frac{1}{10})}^{3}$

Step 1

Multiply ${(\frac{1}{10})}^{2}$ by $\frac{1}{10}$ by adding the exponents.

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Step 1.1

Multiply ${(\frac{1}{10})}^{2}$ by $\frac{1}{10}$ .

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Step 1.1.1

Raise $\frac{1}{10}$ to the power of $1$ .

${(\frac{1}{10})}^{2} \cdot {(\frac{1}{10})}^{1} \cdot {(\frac{1}{10})}^{3}$

Step 1.1.2

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

${(\frac{1}{10})}^{2 + 1} \cdot {(\frac{1}{10})}^{3}$

Step 1.2

Add $2$ and $1$ .

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

Step 2

Multiply ${(\frac{1}{10})}^{3}$ by ${(\frac{1}{10})}^{3}$ 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.

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

Step 2.2

Add $3$ and $3$ .

${(\frac{1}{10})}^{6}$

Step 3

Apply the product rule to $\frac{1}{10}$ .

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

Step 4

One to any power is one.

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

Step 5

Raise $10$ to the power of $6$ .

$\frac{1}{1000000}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{1000000}$

Decimal Form:

$1 \cdot 10^{- 6}$