Question

select all that are equal to $6^{4}(6^{-5}).LXB0square$ $\frac{1}{6}LXB1square$ $\frac{1}{6^{1}}$$square$ $\frac{1}{-6}$done

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \times a^n = a^{m+n}$.
$6^4(6^{-5}) = 6^{4 + (-5)} = 6^{-1}$

Step2: Rewrite negative exponent

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

Step3: Match with options

Compare the simplified result to each option:

• $\frac{1}{6^{-1}} = 6^1 = 6$ (not equal)
• $\frac{1}{6}$ (equal)
• $6^{-1}$ (equal)
• $\frac{1}{6^1} = \frac{1}{6}$ (equal)
• $\frac{1}{-6}$ (not equal)

Answer:

$\frac{1}{6}$, $6^{-1}$, $\frac{1}{6^1}$