Calculus Examples

${(\frac{63}{121})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{63}{121}$ .

$\frac{63^{\frac{3}{2}}}{121^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $121$ as $11^{2}$ .

$\frac{63^{\frac{3}{2}}}{{(11^{2})}^{\frac{3}{2}}}$

Step 2.2

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

$\frac{63^{\frac{3}{2}}}{11^{2 (\frac{3}{2})}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{63^{\frac{3}{2}}}{11^{2 (\frac{3}{2})}}$

Step 2.3.2

Rewrite the expression.

$\frac{63^{\frac{3}{2}}}{11^{3}}$

Step 2.4

Raise $11$ to the power of $3$ .

$\frac{63^{\frac{3}{2}}}{1331}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{63^{\frac{3}{2}}}{1331}$

Decimal Form:

$0.37569271 \dots$