Basic Math Examples

${(\frac{3}{5} - {(- \frac{1}{2})}^{2} + \frac{9}{10})}^{0}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{1}{2}$ .

${(\frac{3}{5} - ({(- 1)}^{2} {(\frac{1}{2})}^{2}) + \frac{9}{10})}^{0}$

Step 1.1.2

Apply the product rule to $\frac{1}{2}$ .

${(\frac{3}{5} - ({(- 1)}^{2} \frac{1^{2}}{2^{2}}) + \frac{9}{10})}^{0}$

Step 1.2

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 1.2.1

Move ${(- 1)}^{2}$ .

${(\frac{3}{5} + {(- 1)}^{2} \cdot - 1 \frac{1^{2}}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.2.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 1.2.2.1

Raise $- 1$ to the power of $1$ .

${(\frac{3}{5} + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{1^{2}}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{3}{5} + {(- 1)}^{2 + 1} \frac{1^{2}}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.2.3

Add $2$ and $1$ .

${(\frac{3}{5} + {(- 1)}^{3} \frac{1^{2}}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.3

Raise $- 1$ to the power of $3$ .

${(\frac{3}{5} - \frac{1^{2}}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.4

One to any power is one.

${(\frac{3}{5} - \frac{1}{2^{2}} + \frac{9}{10})}^{0}$

Step 1.5

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

${(\frac{3}{5} - \frac{1}{4} + \frac{9}{10})}^{0}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3}{5}$ by $\frac{4}{4}$ .

${(\frac{3}{5} \cdot \frac{4}{4} - \frac{1}{4} + \frac{9}{10})}^{0}$

Step 2.2

Multiply $\frac{3}{5}$ by $\frac{4}{4}$ .

${(\frac{3 \cdot 4}{5 \cdot 4} - \frac{1}{4} + \frac{9}{10})}^{0}$

Step 2.3

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

${(\frac{3 \cdot 4}{5 \cdot 4} - (\frac{1}{4} \cdot \frac{5}{5}) + \frac{9}{10})}^{0}$

Step 2.4

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

${(\frac{3 \cdot 4}{5 \cdot 4} - \frac{5}{4 \cdot 5} + \frac{9}{10})}^{0}$

Step 2.5

Multiply $\frac{9}{10}$ by $\frac{2}{2}$ .

${(\frac{3 \cdot 4}{5 \cdot 4} - \frac{5}{4 \cdot 5} + \frac{9}{10} \cdot \frac{2}{2})}^{0}$

Step 2.6

Multiply $\frac{9}{10}$ by $\frac{2}{2}$ .

${(\frac{3 \cdot 4}{5 \cdot 4} - \frac{5}{4 \cdot 5} + \frac{9 \cdot 2}{10 \cdot 2})}^{0}$

Step 2.7

Reorder the factors of $5 \cdot 4$ .

${(\frac{3 \cdot 4}{4 \cdot 5} - \frac{5}{4 \cdot 5} + \frac{9 \cdot 2}{10 \cdot 2})}^{0}$

Step 2.8

Multiply $4$ by $5$ .

${(\frac{3 \cdot 4}{20} - \frac{5}{4 \cdot 5} + \frac{9 \cdot 2}{10 \cdot 2})}^{0}$

Step 2.9

Multiply $4$ by $5$ .

${(\frac{3 \cdot 4}{20} - \frac{5}{20} + \frac{9 \cdot 2}{10 \cdot 2})}^{0}$

Step 2.10

Reorder the factors of $10 \cdot 2$ .

${(\frac{3 \cdot 4}{20} - \frac{5}{20} + \frac{9 \cdot 2}{2 \cdot 10})}^{0}$

Step 2.11

Multiply $2$ by $10$ .

${(\frac{3 \cdot 4}{20} - \frac{5}{20} + \frac{9 \cdot 2}{20})}^{0}$

Step 3

Combine the numerators over the common denominator.

${(\frac{3 \cdot 4 - 5 + 9 \cdot 2}{20})}^{0}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $4$ .

${(\frac{12 - 5 + 9 \cdot 2}{20})}^{0}$

Step 4.2

Multiply $9$ by $2$ .

${(\frac{12 - 5 + 18}{20})}^{0}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $5$ from $12$ .

${(\frac{7 + 18}{20})}^{0}$

Step 5.2

Add $7$ and $18$ .

${(\frac{25}{20})}^{0}$

Step 5.3

Cancel the common factor of $25$ and $20$ .

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Step 5.3.1

Factor $5$ out of $25$ .

${(\frac{5 (5)}{20})}^{0}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $5$ out of $20$ .

${(\frac{5 \cdot 5}{5 \cdot 4})}^{0}$

Step 5.3.2.2

Cancel the common factor.

${(\frac{5 \cdot 5}{5 \cdot 4})}^{0}$

Step 5.3.2.3

Rewrite the expression.

${(\frac{5}{4})}^{0}$

Step 5.4

Simplify the expression.

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Step 5.4.1

Apply the product rule to $\frac{5}{4}$ .

$\frac{5^{0}}{4^{0}}$

Step 5.4.2

Anything raised to $0$ is $1$ .

$\frac{1}{4^{0}}$

Step 5.4.3

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 5.4.4

Divide $1$ by $1$ .

$1$