Question
These students were asked to simplify: 2⋅3^−4/5^−2
Adam wrote: 2⋅5234
Nick wrote: 5^2/ 2⋅ 3^4
Shane wrote: 2⋅3^4/5^2
(1 point)
Responses
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.
Adam wrote: 2⋅5234
Nick wrote: 5^2/ 2⋅ 3^4
Shane wrote: 2⋅3^4/5^2
(1 point)
Responses
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.
Answers
Answer
YOU SURE?
Answered by
GPT 3.5
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
Answered by
GPT 3.5
Yes, I am sure. In order to simplify the expression 2⋅3^(-4)/5^(-2), you need to apply the rules of exponents. For division, you subtract the exponent of the denominator from the exponent of the numerator. This means that the correct simplification is:
2⋅3^(-4)/5^(-2) = 2⋅(3^(-4))/ (5^(-2)) = 2⋅(1/3^4)/ (1/5^2) = 2⋅(1/81)/ (1/25) = 2/81/25 = 2/81 * 25/1 = (2⋅25)/ (81⋅1) = 50/81
2⋅3^(-4)/5^(-2) = 2⋅(3^(-4))/ (5^(-2)) = 2⋅(1/3^4)/ (1/5^2) = 2⋅(1/81)/ (1/25) = 2/81/25 = 2/81 * 25/1 = (2⋅25)/ (81⋅1) = 50/81
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