Question

16 which expression is equivalent to \\(\frac{c^{8}(d^{6})^{3}}{c^{2}}\\) for all values of c for which the expression is defined?\
f \\(c^{4}d^{9}\\)\
g \\(c^{4}d^{18}\\)\
h \\(c^{6}d^{9}\\)\
j \\(c^{6}d^{18}\\)\
\\(\bigcirc\\) f\
\\(\bigcirc\\) g\
\\(\bigcirc\\) h\
\\(\bigcirc\\) j

Explanation:

Step1: Simplify the exponent of \( d \)

Using the power of a power rule \((a^m)^n = a^{m \times n}\), for \((d^6)^3\), we have \(d^{6\times3}=d^{18}\). So the numerator becomes \(c^8d^{18}\).

Step2: Simplify the exponents of \( c \)

Using the quotient of powers rule \(\frac{a^m}{a^n}=a^{m - n}\), for \(\frac{c^8}{c^2}\), we have \(c^{8 - 2}=c^6\).

Step3: Combine the results

Combining the simplified \( c \) and \( d \) terms, we get \(c^6d^{18}\).

Answer:

J. \( c^6d^{18} \)