Evaluate (49/64)^(1/2)

${(\frac{49}{64})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{49}{64}$ .

$\frac{49^{\frac{1}{2}}}{64^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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

$\frac{{(7^{2})}^{\frac{1}{2}}}{64^{\frac{1}{2}}}$

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

$\frac{7^{2 (\frac{1}{2})}}{64^{\frac{1}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7^{2 (\frac{1}{2})}}{64^{\frac{1}{2}}}$

Rewrite the expression.

$\frac{7^{1}}{64^{\frac{1}{2}}}$

Evaluate the exponent.

$\frac{7}{64^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$\frac{7}{{(8^{2})}^{\frac{1}{2}}}$

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

$\frac{7}{8^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7}{8^{2 (\frac{1}{2})}}$

Rewrite the expression.

$\frac{7}{8^{1}}$

Evaluate the exponent.

$\frac{7}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$