Question

which expression is equivalent to \\(\frac{16k^9m^7}{4k^3m^{14}}\\) for all values of \\(k\\) and \\(m\\) where the expression is defined?\
\
a \\(\frac{12k^6}{m^7}\\)\
\
b \\(\frac{4k^6}{m^7}\\)\
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c \\(\frac{12k^3}{m^2}\\)\
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d \\(\frac{4k^3}{m^2}\\)\
\
\\(\bigcirc\\) c\
\\(\bigcirc\\) b\
\\(\bigcirc\\) a\
\\(\bigcirc\\) d

Explanation:

Step1: Simplify the constant terms

$\frac{16}{4} = 4$

Step2: Simplify the $k$ terms

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$k^{9-3}=k^6$

Step3: Simplify the $m$ terms

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$m^{7-14}=m^{-7}=\frac{1}{m^7}$

Step4: Combine all simplified parts

$4 \times k^6 \times \frac{1}{m^7} = \frac{4k^6}{m^7}$

Answer:

B. $\frac{4k^6}{m^7}$