Basic Math Examples

${(\frac{3 \cdot 3140}{3.14 \cdot 30})}^{\frac{1}{2}}$

Step 1

Cancel the common factor of $3$ and $30$ .

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Step 1.1

Factor $3$ out of $3 \cdot 3140$ .

${(\frac{3 (3140)}{3.14 \cdot 30})}^{\frac{1}{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3.14 \cdot 30$ .

${(\frac{3 (3140)}{3 (1.04\overline{6} \cdot 30)})}^{\frac{1}{2}}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 \cdot 3140}{3 (1.04\overline{6} \cdot 30)})}^{\frac{1}{2}}$

Step 1.2.3

Rewrite the expression.

${(\frac{3140}{1.04\overline{6} \cdot 30})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $3140$ and $30$ .

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Step 2.1

Factor $10$ out of $3140$ .

${(\frac{10 (314)}{1.04\overline{6} \cdot 30})}^{\frac{1}{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $10$ out of $1.04\overline{6} \cdot 30$ .

${(\frac{10 (314)}{10 (0.104\overline{6} \cdot 30)})}^{\frac{1}{2}}$

Step 2.2.2

Cancel the common factor.

${(\frac{10 \cdot 314}{10 (0.104\overline{6} \cdot 30)})}^{\frac{1}{2}}$

Step 2.2.3

Rewrite the expression.

${(\frac{314}{0.104\overline{6} \cdot 30})}^{\frac{1}{2}}$

Step 3

Cancel the common factor of $314$ and $30$ .

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Step 3.1

Factor $2$ out of $314$ .

${(\frac{2 (157)}{0.104\overline{6} \cdot 30})}^{\frac{1}{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $0.104\overline{6} \cdot 30$ .

${(\frac{2 (157)}{2 (0.052\overline{3} \cdot 30)})}^{\frac{1}{2}}$

Step 3.2.2

Cancel the common factor.

${(\frac{2 \cdot 157}{2 (0.052\overline{3} \cdot 30)})}^{\frac{1}{2}}$

Step 3.2.3

Rewrite the expression.

${(\frac{157}{0.052\overline{3} \cdot 30})}^{\frac{1}{2}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $0.052\overline{3}$ by $30$ .

${(\frac{157}{1.57})}^{\frac{1}{2}}$

Step 4.2

Divide $157$ by $1.57$ .

$100^{\frac{1}{2}}$

Step 4.3

Rewrite $100$ as $10^{2}$ .

${(10^{2})}^{\frac{1}{2}}$

Step 4.4

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

$10^{2 (\frac{1}{2})}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$10^{2 (\frac{1}{2})}$

Step 5.2

Rewrite the expression.

$10^{1}$

Step 6

Evaluate the exponent.

$10$