Simplify: (3 ^ 2 * 3 ^ - 1)/(5 ^ - 2 * 2 ^ 0)
Adam wrote: (3 ^ - 2 * 5 ^ 2)/2
Nick wrote: 3 * 5 ^ 2
Shane wrote: (3 ^ - 2)/(5 ^ 3)
Who was correct and why?
(1 point)
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Shane is correct because all that needs to be done is to make the negative exponents positive.
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.
None of these options is correct.
To simplify the expression, we first combine the exponents in the numerator and denominator. This gives us:
(3^2 * 3^-1) / (5^-2 * 2^0)
= 3^1 / 5^-2
Next, we apply the rule that a^-n = 1/a^n:
= 3^1 / (1/5^2)
= 3 / (1/25)
= 3 * 25
= 75
Therefore, none of the students provided the correct simplified expression. The correct answer is 75.