Question

which expression is not equivalent to $\frac{6^{3}}{6^{6}}$?
a $\frac{1}{6^{2}}$
b $6^{-3}$
c $\frac{1}{216}$
d $\frac{1}{6^{3}}$

Explanation:

Step1: Simplify the given expression

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

Step2: Rewrite as positive exponent

Use rule $x^{-a}=\frac{1}{x^a}$
$6^{-3}=\frac{1}{6^3}=\frac{1}{216}$

Step3: Compare with options

Check each option against the simplified result:

• Option A: $\frac{1}{6^2}=\frac{1}{36}

eq \frac{1}{216}$

• Option B: $6^{-3}$ matches Step1 result
• Option C: $\frac{1}{216}$ matches Step2 result
• Option D: $\frac{1}{6^3}=\frac{1}{216}$ matches Step2 result

Answer:

A. $\frac{1}{6^2}$