Basic Math Examples

${(\frac{6^{- 1} \cdot 7^{2}}{6^{2} \cdot 7^{- 4}})}^{\frac{7}{2}}$

Step 1

Move $6^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{7^{2}}{6^{2} \cdot 7^{- 4} \cdot 6})}^{\frac{7}{2}}$

Step 2

Multiply $6^{2}$ by $6$ by adding the exponents.

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Step 2.1

Move $6$ .

${(\frac{7^{2}}{6 \cdot 6^{2} \cdot 7^{- 4}})}^{\frac{7}{2}}$

Step 2.2

Multiply $6$ by $6^{2}$ .

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Step 2.2.1

Raise $6$ to the power of $1$ .

${(\frac{7^{2}}{6^{1} \cdot 6^{2} \cdot 7^{- 4}})}^{\frac{7}{2}}$

Step 2.2.2

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

${(\frac{7^{2}}{6^{1 + 2} \cdot 7^{- 4}})}^{\frac{7}{2}}$

Step 2.3

Add $1$ and $2$ .

${(\frac{7^{2}}{6^{3} \cdot 7^{- 4}})}^{\frac{7}{2}}$

Step 3

Move $7^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{7^{2} \cdot 7^{4}}{6^{3}})}^{\frac{7}{2}}$

Step 4

Multiply $7^{2}$ by $7^{4}$ by adding the exponents.

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Step 4.1

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

${(\frac{7^{2 + 4}}{6^{3}})}^{\frac{7}{2}}$

Step 4.2

Add $2$ and $4$ .

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

Step 5

Simplify the expression.

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Step 5.1

Raise $7$ to the power of $6$ .

${(\frac{117649}{6^{3}})}^{\frac{7}{2}}$

Step 5.2

Raise $6$ to the power of $3$ .

${(\frac{117649}{216})}^{\frac{7}{2}}$

Step 5.3

Apply the product rule to $\frac{117649}{216}$ .

$\frac{117649^{\frac{7}{2}}}{216^{\frac{7}{2}}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $117649$ as $343^{2}$ .

$\frac{{(343^{2})}^{\frac{7}{2}}}{216^{\frac{7}{2}}}$

Step 6.2

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

$\frac{343^{2 (\frac{7}{2})}}{216^{\frac{7}{2}}}$

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Cancel the common factor.

$\frac{343^{2 (\frac{7}{2})}}{216^{\frac{7}{2}}}$

Step 6.3.2

Rewrite the expression.

$\frac{343^{7}}{216^{\frac{7}{2}}}$

Step 6.4

Raise $343$ to the power of $7$ .

$\frac{558545864083284000}{216^{\frac{7}{2}}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{558545864083284000}{216^{\frac{7}{2}}}$

Decimal Form:

$3771123117.78509$