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? (1 point) Responses
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.
B. None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
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, we can use the rules of exponents.
First, we have 3^2 × 3^(-1) / 5^(-2) × 2^0.
We know that a^m × a^n = a^(m+n), so we can combine the exponents of 3:
3^2 × 3^(-1) = 3^(2+(-1)) = 3^1 = 3
Next, 5^(-2) means 1/5^2. Using the rule a^(-n) = 1/a^n, we can rewrite it as:
1/5^2 = 5^(-2)
Lastly, any number raised to the power of 0 is always 1, so 2^0 = 1.
Substituting these back into the original expression, we have:
3 × 5^(-2) × 1 = 3/5^2
Therefore, out of the options given, Shane is correct. He simplified the expression to 3^(-3)/5^2, which is another way of writing 3/5^2.