Basic Math Examples

${(11^{\frac{2}{3}})}^{6} \cdot (\frac{11^{7}}{11^{7}}) \cdot (\frac{11^{7}}{11^{7}} \cdot (11^{3} \cdot 11^{3}))$

Step 1

Multiply $11^{3}$ by $11^{3}$ by adding the exponents.

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Step 1.1

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

${(11^{\frac{2}{3}})}^{6} \cdot (\frac{11^{7}}{11^{7}}) \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{3 + 3})$

Step 1.2

Add $3$ and $3$ .

${(11^{\frac{2}{3}})}^{6} \cdot (\frac{11^{7}}{11^{7}}) \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 2

Cancel the common factor of $11^{7}$ .

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Step 2.1

Cancel the common factor.

${(11^{\frac{2}{3}})}^{6} \cdot \frac{11^{7}}{11^{7}} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 2.2

Rewrite the expression.

${(11^{\frac{2}{3}})}^{6} \cdot 1 \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3

Simplify the expression.

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Step 3.1

Multiply ${(11^{\frac{2}{3}})}^{6}$ by $1$ .

${(11^{\frac{2}{3}})}^{6} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3.2

Multiply the exponents in ${(11^{\frac{2}{3}})}^{6}$ .

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Step 3.2.1

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

$11^{\frac{2}{3} \cdot 6} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Factor $3$ out of $6$ .

$11^{\frac{2}{3} \cdot (3 (2))} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3.2.2.2

Cancel the common factor.

$11^{\frac{2}{3} \cdot (3 \cdot 2)} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3.2.2.3

Rewrite the expression.

$11^{2 \cdot 2} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 3.2.3

Multiply $2$ by $2$ .

$11^{4} \cdot (\frac{11^{7}}{11^{7}} \cdot 11^{6})$

Step 4

Multiply $11^{4}$ by $11^{6}$ by adding the exponents.

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Step 4.1

Move $11^{6}$ .

$11^{6} \cdot 11^{4} \cdot \frac{11^{7}}{11^{7}}$

Step 4.2

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

$11^{6 + 4} \cdot \frac{11^{7}}{11^{7}}$

Step 4.3

Add $6$ and $4$ .

$11^{10} \cdot \frac{11^{7}}{11^{7}}$

Step 5

Cancel the common factor of $11^{7}$ .

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Step 5.1

Cancel the common factor.

$11^{10} \cdot \frac{11^{7}}{11^{7}}$

Step 5.2

Rewrite the expression.

$11^{10} \cdot 1$

Step 6

Simplify the expression.

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Step 6.1

Multiply $11^{10}$ by $1$ .

$11^{10}$

Step 6.2

Raise $11$ to the power of $10$ .

$25937424601$