Question

which expression is equivalent to \\(\frac{4^{6}}{4^{6}}\\)?
\\(4\\) \\(4^{-8}\cdot 4^{8}\\) \\((4^{6})^{-5}\\) \\(\frac{1}{4}\\)

Explanation:

Step1: Simplify the original expression

When dividing exponents with the same base, subtract the exponents: $\frac{4^6}{4^6} = 4^{6-6} = 4^0 = 1$

Step2: Evaluate each option

• Option 1: $4

eq 1$

• Option 2: When multiplying exponents with the same base, add the exponents: $4^{-8} \cdot 4^8 = 4^{-8+8} = 4^0 = 1$
• Option 3: For a power of a power, multiply exponents: $(4^6)^{-5} = 4^{6 \times (-5)} = 4^{-30}

eq 1$

• Option 4: $\frac{1}{4}

eq 1$

Answer:

$4^{-8} \cdot 4^8$