Basic Math Examples

${(\frac{1}{256})}^{\frac{1}{4}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{256}$ .

$\frac{1^{\frac{1}{4}}}{256^{\frac{1}{4}}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.2

One to any power is one.

$\frac{1}{256^{\frac{1}{4}}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $256$ as $4^{4}$ .

$\frac{1}{{(4^{4})}^{\frac{1}{4}}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.3.2

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

$\frac{1}{4^{4 (\frac{1}{4})}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.3.3

Cancel the common factor of $4$ .

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Step 1.3.3.1

Cancel the common factor.

$\frac{1}{4^{4 (\frac{1}{4})}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.3.3.2

Rewrite the expression.

$\frac{1}{4^{1}} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.3.4

Evaluate the exponent.

$\frac{1}{4} + {(9)}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.4

Rewrite $9$ as $3^{2}$ .

$\frac{1}{4} + {(3^{2})}^{\frac{1}{2}} + {0.2}^{0} - 1^{20}$

Step 1.5

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

$\frac{1}{4} + 3^{2 (\frac{1}{2})} + {0.2}^{0} - 1^{20}$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Cancel the common factor.

$\frac{1}{4} + 3^{2 (\frac{1}{2})} + {0.2}^{0} - 1^{20}$

Step 1.6.2

Rewrite the expression.

$\frac{1}{4} + 3^{1} + {0.2}^{0} - 1^{20}$

Step 1.7

Evaluate the exponent.

$\frac{1}{4} + 3 + {0.2}^{0} - 1^{20}$

Step 1.8

Anything raised to $0$ is $1$ .

$\frac{1}{4} + 3 + 1 - 1^{20}$

Step 1.9

One to any power is one.

$\frac{1}{4} + 3 + 1 - 1 \cdot 1$

Step 1.10

Multiply $- 1$ by $1$ .

$\frac{1}{4} + 3 + 1 - 1$

Step 2

Find the common denominator.

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Step 2.1

Write $3$ as a fraction with denominator $1$ .

$\frac{1}{4} + \frac{3}{1} + 1 - 1$

Step 2.2

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3}{1} \cdot \frac{4}{4} + 1 - 1$

Step 2.3

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + 1 - 1$

Step 2.4

Write $1$ as a fraction with denominator $1$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{1}{1} - 1$

Step 2.5

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{1}{1} \cdot \frac{4}{4} - 1$

Step 2.6

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{4}{4} - 1$

Step 2.7

Write $- 1$ as a fraction with denominator $1$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{4}{4} + \frac{- 1}{1}$

Step 2.8

Multiply $\frac{- 1}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{4}{4} + \frac{- 1}{1} \cdot \frac{4}{4}$

Step 2.9

Multiply $\frac{- 1}{1}$ by $\frac{4}{4}$ .

$\frac{1}{4} + \frac{3 \cdot 4}{4} + \frac{4}{4} + \frac{- 1 \cdot 4}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 + 3 \cdot 4 + 4 - 1 \cdot 4}{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $4$ .

$\frac{1 + 12 + 4 - 1 \cdot 4}{4}$

Step 4.2

Multiply $- 1$ by $4$ .

$\frac{1 + 12 + 4 - 4}{4}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $1$ and $12$ .

$\frac{13 + 4 - 4}{4}$

Step 5.2

Add $13$ and $4$ .

$\frac{17 - 4}{4}$

Step 5.3

Subtract $4$ from $17$ .

$\frac{13}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{4}$

Decimal Form:

$3.25$

Mixed Number Form:

$3 \frac{1}{4}$