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)
Shane is correct because all that needs to be done is to make the negative exponents positive.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
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.
5 answers
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division. When simplified correctly, the expression is 3.
(3^2 × 3^−1) / (5^−2 × 2^0 )
(9 / 3) * (25 / 1)
75
so I am inclined to agree with Nick
However I am just guessing about what is numerator and what is denominator.
(9 / 3) * (25 / 1)
75
so I am inclined to agree with Nick
However I am just guessing about what is numerator and what is denominator.
Let's simplify the expression step by step to clarify:
First, we simplify inside each set of parentheses:
3^2 × 3^−1 = 3^(2-1) = 3^1 = 3
5^−2 × 2^0 = 1/5^2 * 1 = 1/25
Now, we divide the results:
(3)/(1/25)
= 3 * 25
= 75
Therefore, Shane was correct in simplifying the expression to 3^−3 / 5^2, which simplifies to 75.
First, we simplify inside each set of parentheses:
3^2 × 3^−1 = 3^(2-1) = 3^1 = 3
5^−2 × 2^0 = 1/5^2 * 1 = 1/25
Now, we divide the results:
(3)/(1/25)
= 3 * 25
= 75
Therefore, Shane was correct in simplifying the expression to 3^−3 / 5^2, which simplifies to 75.
That was Nick not Shane
Apologies for the confusion. You are correct, Nick was correct in simplifying the expression to 3 * 5^2, which simplifies to 75. Thank you for pointing that out.
5 answers