Pre-Algebra Examples

${(\frac{1}{1000})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{1}{1000}$ .

$\frac{1^{\frac{2}{3}}}{1000^{\frac{2}{3}}}$

Step 1.2

One to any power is one.

$\frac{1}{1000^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1000$ as $10^{3}$ .

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

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

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

$\frac{1}{100}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{100}$

Decimal Form:

$0.01$