Basic Math Examples

${(\frac{23100}{16000})}^{\frac{1}{5}} - 1$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $23100$ and $16000$ .

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Step 1.1.1

Factor $100$ out of $23100$ .

${(\frac{100 (231)}{16000})}^{\frac{1}{5}} - 1$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $100$ out of $16000$ .

${(\frac{100 \cdot 231}{100 \cdot 160})}^{\frac{1}{5}} - 1$

Step 1.1.2.2

Cancel the common factor.

${(\frac{100 \cdot 231}{100 \cdot 160})}^{\frac{1}{5}} - 1$

Step 1.1.2.3

Rewrite the expression.

${(\frac{231}{160})}^{\frac{1}{5}} - 1$

Step 1.2

Apply the product rule to $\frac{231}{160}$ .

$\frac{231^{\frac{1}{5}}}{160^{\frac{1}{5}}} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$ .

$\frac{231^{\frac{1}{5}}}{160^{\frac{1}{5}}} - 1 \cdot \frac{160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$

Step 3

Combine $- 1$ and $\frac{160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$ .

$\frac{231^{\frac{1}{5}}}{160^{\frac{1}{5}}} + \frac{- 160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{231^{\frac{1}{5}} - 160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{231^{\frac{1}{5}} - 160^{\frac{1}{5}}}{160^{\frac{1}{5}}}$

Decimal Form:

$0.07621341 \dots$