Question

negative / zero exponents (level 1)
this is the only question in this section.
question
which expression is equivalent to \\(\frac{6^{-2}}{6^{-1}}\\)?
answer
\\(\circ\\) 1 \\(\circ\\) 6
\\(\circ\\) 36 \\(\circ\\) \\(\frac{1}{6}\\)

Explanation:

Step1: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $\frac{a^m}{a^n}=a^{m-n}$. So $\frac{6^{-2}}{6^{-1}}=6^{-2-(-1)}$

Step2: Simplify the exponent

Calculate the exponent: $6^{-2+1}=6^{-1}$

Step3: Rewrite negative exponent

A negative exponent means reciprocal: $6^{-1}=\frac{1}{6}$

Answer:

$\frac{1}{6}$