Basic Math Examples

${(\frac{13000}{9000})}^{\frac{1}{3}} - 1$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $13000$ and $9000$ .

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Step 1.1.1

Factor $1000$ out of $13000$ .

${(\frac{1000 (13)}{9000})}^{\frac{1}{3}} - 1$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $1000$ out of $9000$ .

${(\frac{1000 \cdot 13}{1000 \cdot 9})}^{\frac{1}{3}} - 1$

Step 1.1.2.2

Cancel the common factor.

${(\frac{1000 \cdot 13}{1000 \cdot 9})}^{\frac{1}{3}} - 1$

Step 1.1.2.3

Rewrite the expression.

${(\frac{13}{9})}^{\frac{1}{3}} - 1$

Step 1.2

Apply the product rule to $\frac{13}{9}$ .

$\frac{13^{\frac{1}{3}}}{9^{\frac{1}{3}}} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$ .

$\frac{13^{\frac{1}{3}}}{9^{\frac{1}{3}}} - 1 \cdot \frac{9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$

Step 3

Combine $- 1$ and $\frac{9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$ .

$\frac{13^{\frac{1}{3}}}{9^{\frac{1}{3}}} + \frac{- 9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{13^{\frac{1}{3}} - 9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13^{\frac{1}{3}} - 9^{\frac{1}{3}}}{9^{\frac{1}{3}}}$

Decimal Form:

$0.13040381 \dots$