Evaluate (16/49)^(-1/2)

${(\frac{16}{49})}^{- \frac{1}{2}}$

Step 1

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

${(\frac{49}{16})}^{\frac{1}{2}}$

Step 2

Apply the product rule to $\frac{49}{16}$ .

$\frac{49^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 3

Simplify the numerator.

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

$\frac{{(7^{2})}^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

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

$\frac{7^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{7^{1}}{16^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{7}{16^{\frac{1}{2}}}$

Step 4

Simplify the denominator.

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

$\frac{7}{{(4^{2})}^{\frac{1}{2}}}$

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

$\frac{7}{4^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7}{4^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{7}{4^{1}}$

Evaluate the exponent.

$\frac{7}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{4}$

Decimal Form:

$1.75$

Mixed Number Form:

$1 \frac{3}{4}$