Which of the following is an equivalent expression to 7325−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
Responses
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
73⋅254
7 cubed times 25 superscript 4 baseline
25473
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction
2547−3
The correct equivalent expression with only positive exponents, generated by applying the Property of Negative Integer Exponents, is:
Start Fraction 25 superscript 4 over 7 cubed end fraction
To generate an equivalent expression with only positive exponents by applying the Property of Negative Integer Exponents, we need to move the negative exponent from the denominator to the numerator.
Out of the given options, the expression that achieves this is:
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction
To find the equivalent expression with only positive exponents, we need to apply the Property of Negative Integer Exponents. According to this property, any term raised to a negative exponent can be rewritten as the reciprocal of the term raised to the positive exponent.
In this case, the original expression is 7325−4.
To remove the negative exponent, we can rewrite 25−4 as 1/254. This is done by taking the reciprocal of 25 (25−1) and changing the sign of the exponent.
So, the equivalent expression with only positive exponents is:
7325−4 = 73×1/254 = 73254.
Therefore, the correct answer is 73254.