Evaluate (9/16)^(-1/2)

${(\frac{9}{16})}^{- \frac{1}{2}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{16}{9})}^{\frac{1}{2}}$

Step 2

Apply the product rule to $\frac{16}{9}$ .

$\frac{16^{\frac{1}{2}}}{9^{\frac{1}{2}}}$

Step 3

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{{(4^{2})}^{\frac{1}{2}}}{9^{\frac{1}{2}}}$

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

$\frac{4^{2 (\frac{1}{2})}}{9^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4^{2 (\frac{1}{2})}}{9^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{4^{1}}{9^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{4}{9^{\frac{1}{2}}}$

Step 4

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{4}{{(3^{2})}^{\frac{1}{2}}}$

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

$\frac{4}{3^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4}{3^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{4}{3^{1}}$

Evaluate the exponent.

$\frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$