Which of the following is an equivalent expression to 7325−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
25473
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
73⋅254
7 cubed times 25 superscript 4 baseline
73254
Start Fraction 7 cubed times 25 superscript 4 baseline end fraction
To find an equivalent expression with only positive exponents by applying the Property of Negative Integer Exponents, we need to move any negative exponents to the denominator or numerator depending on their sign.
Starting with the expression 7325−4, the negative exponent means that the term should be moved to the denominator. Thus, the equivalent expression would be:
7325−4 = (7^3)/(25^4)
So, the correct answer is Start Fraction 23 superscript 7 baseline over 25 superscript 4 baseline.
To find an equivalent expression to 7325−4 with only positive exponents using the Property of Negative Integer Exponents, we need to apply the rule which states that any term with a negative exponent can be flipped to the denominator with the positive exponent.
In this case, the term with the negative exponent is 7-4. To flip this term to the denominator, we can make the exponent positive by placing it in the denominator as 1/7^4.
Therefore, an equivalent expression would be:
7325−4 = 7325 ÷ 1/7^4
Simplifying this expression, we multiply the numerator by the reciprocal of the denominator:
7325 ÷ 1/7^4 = 7325 × 7^4
So, the equivalent expression is 7325 × 7^4, which can be written as "73⋅254"