Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
responses
7^3 ⋅ 25^4
7^3/25^4
25^4/7^3
25^4/7^-3
The equivalent expression, generated by applying the Property of Negative Integer Exponents, is 7^3 ⋅ 25^4.
To rewrite the expression 7^3/25^-4 with only positive exponents, we can apply the Property of Negative Integer Exponents. According to this property, any term with a negative exponent can be moved to the denominator and have its exponent changed to positive.
Therefore, the equivalent expression would be 7^3 ⋅ 25^4.
To find an equivalent expression with only positive exponents using the Property of Negative Integer Exponents, we need to apply the rule that a^(-b) equals 1 / a^b.
The given expression is 7^3 / 25^(-4).
To apply the property, we can rewrite 25^(-4) as 1 / 25^4.
Substituting this back into the expression, we have 7^3 / (1 / 25^4).
Next, we'll use the rule that a / (1/b) equals a * b. By applying this rule, we can rewrite the expression as 7^3 * 25^4.
Therefore, the correct equivalent expression with only positive exponents is 7^3 * 25^4.
Answer: 7^3 * 25^4