Multiply Powers with Base 5: Solving 5^(-8) × 5^6

Insert the corresponding expression:

$$$5^{-8}\times5^6=$

Let's simplify the expression $5^{-8} \times 5^6$ using the rules of exponents.

• Step 1: Apply the rule for multiplying powers with the same base. According to this rule, when multiplying like bases, we add the exponents: $5^{-8} \times 5^6 = 5^{-8 + 6}$
• Step 2: Calculate the sum of the exponents: $-8 + 6 = -2$.
• Step 3: Write the simplified expression: $5^{-2}$.
• Step 4: Relate the expression to the given choices:

The simplified expression $5^{-2}$ corresponds to choice 1. Additionally, rewriting a negative exponent using the fraction format gives: $5^{-2} = \frac{1}{5^2}$, which matches choice 2.

Thus, both choices 'a: $5^{-2}$' and 'b: $\frac{1}{5^2}$' are correct.

Therefore, according to the given answer choice, a'+b' are correct.