Evaluate (27/1000)^(2/3)

${(\frac{27}{1000})}^{\frac{2}{3}}$

Step 1

Apply the product rule to $\frac{27}{1000}$ .

$\frac{27^{\frac{2}{3}}}{1000^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

Rewrite $27$ as $3^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $3$ to the power of $2$ .

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

Step 3

Simplify the denominator.

Rewrite $1000$ as $10^{3}$ .

$\frac{9}{{(10^{3})}^{\frac{2}{3}}}$

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

$\frac{9}{10^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{9}{10^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{9}{10^{2}}$

Raise $10$ to the power of $2$ .

$\frac{9}{100}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{100}$

Decimal Form:

$0.09$