Simplify: 3^2×3^−1/5^−2×2^0
Adam wrote: 3^−2×5^2/2
Nick wrote 3×5^2
Shane wrote: 3^−3/5^2
Who was correct and why?
A. Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.
C. Shane is correct because all that needs to be done is to make the negative exponents positive.
D. Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
To simplify the expression 3^2 × 3^(-1) / 5^(-2) × 2^0, we can use the exponent rules:
1. When multiplying with the same base, we add the exponents. So, 3^2 × 3^(-1) simplifies to 3^(2 + (-1)) = 3^1 = 3.
2. When dividing with the same base, we subtract the exponents. So, 5^(-2) simplifies to 1 / 5^2.
Substituting these simplifications back into the expression, we have 3 × (1 / 5^2) × 2^0 = 3 / 25 × 1 = 3 / 25.
None of the options presented match the simplified expression. Therefore, none of Adam, Nick, or Shane is correct.