Basic Math Examples

${(\frac{12900}{9000})}^{\frac{1}{4}} - 1$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $12900$ and $9000$ .

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Step 1.1.1

Factor $300$ out of $12900$ .

${(\frac{300 (43)}{9000})}^{\frac{1}{4}} - 1$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $300$ out of $9000$ .

${(\frac{300 \cdot 43}{300 \cdot 30})}^{\frac{1}{4}} - 1$

Step 1.1.2.2

Cancel the common factor.

${(\frac{300 \cdot 43}{300 \cdot 30})}^{\frac{1}{4}} - 1$

Step 1.1.2.3

Rewrite the expression.

${(\frac{43}{30})}^{\frac{1}{4}} - 1$

Step 1.2

Apply the product rule to $\frac{43}{30}$ .

$\frac{43^{\frac{1}{4}}}{30^{\frac{1}{4}}} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$ .

$\frac{43^{\frac{1}{4}}}{30^{\frac{1}{4}}} - 1 \cdot \frac{30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$

Step 3

Combine $- 1$ and $\frac{30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$ .

$\frac{43^{\frac{1}{4}}}{30^{\frac{1}{4}}} + \frac{- 30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{43^{\frac{1}{4}} - 30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{43^{\frac{1}{4}} - 30^{\frac{1}{4}}}{30^{\frac{1}{4}}}$

Decimal Form:

$0.09417503 \dots$