Evaluate (36/49)^(3/2)

${(\frac{36}{49})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{36}{49}$ .

$\frac{36^{\frac{3}{2}}}{49^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{{(6^{2})}^{\frac{3}{2}}}{49^{\frac{3}{2}}}$

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

$\frac{6^{2 (\frac{3}{2})}}{49^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{6^{2 (\frac{3}{2})}}{49^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{6^{3}}{49^{\frac{3}{2}}}$

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

$\frac{216}{49^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{216}{{(7^{2})}^{\frac{3}{2}}}$

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

$\frac{216}{7^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{216}{7^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{216}{7^{3}}$

Raise $7$ to the power of $3$ .

$\frac{216}{343}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{216}{343}$

Decimal Form:

$0.62973760 \dots$