Question

simplify
\\(\frac{m^{\frac{5}{8}}}{m^{\frac{1}{8}}}\\)
options:
a. \\(m^4\\)
b. \\(m^{\frac{3}{4}}\\)
c. \\(m^{\frac{5}{64}}\\)
d. \\(m^{\frac{1}{2}}\\)

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $\frac{m^a}{m^b}=m^{a-b}$. Here, $a=\frac{5}{8}$, $b=\frac{1}{8}$.
$\frac{m^{\frac{5}{8}}}{m^{\frac{1}{8}}}=m^{\frac{5}{8}-\frac{1}{8}}$

Step2: Subtract the fractions

Calculate the exponent difference.
$m^{\frac{5-1}{8}}=m^{\frac{4}{8}}$

Step3: Simplify the fraction

Reduce the exponent to lowest terms.
$m^{\frac{1}{2}}$

Answer:

d. $m^{\frac{1}{2}}$