Evaluate (100/81)^(3/2)

${(\frac{100}{81})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $\frac{100}{81}$ .

$\frac{100^{\frac{3}{2}}}{81^{\frac{3}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(10^{2})}^{\frac{3}{2}}}{81^{\frac{3}{2}}}$

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

$\frac{10^{2 (\frac{3}{2})}}{81^{\frac{3}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{10^{2 (\frac{3}{2})}}{81^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{10^{3}}{81^{\frac{3}{2}}}$

Raise $10$ to the power of $3$ .

$\frac{1000}{81^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$\frac{1000}{{(9^{2})}^{\frac{3}{2}}}$

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

$\frac{1000}{9^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1000}{9^{2 (\frac{3}{2})}}$

Rewrite the expression.

$\frac{1000}{9^{3}}$

Raise $9$ to the power of $3$ .

$\frac{1000}{729}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1000}{729}$

Decimal Form:

$1.37174211 \dots$

Mixed Number Form:

$1 \frac{271}{729}$