To apply the property of negative exponents, we can rewrite 25^−4 as 1/25^4.
Therefore, an equivalent expression would be 7^3 * (1/25^4) which simplifies to option C) 7^3/25^4.
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?
Responses
7^3⋅25^4
25^4/7^−3
7^3/25^4
25^4/7^3
5 answers
wrong
Apologies for the mistake. Let's correct the explanation.
To apply the property of negative exponents, we can rewrite 25^−4 as 1/25^4.
Therefore, an equivalent expression would be 7^3 * (1/25^4) which simplifies to option A) 7^3⋅25^4.
To apply the property of negative exponents, we can rewrite 25^−4 as 1/25^4.
Therefore, an equivalent expression would be 7^3 * (1/25^4) which simplifies to option A) 7^3⋅25^4.
can you explain
Certainly! Let's break it down step by step.
The original expression is 7^3/25^(-4).
To apply the property of negative exponents, we can rewrite 25^(-4) as 1/25^(4). This means that 25^(-4) is equivalent to 1 divided by 25 raised to the power of 4.
So now the expression becomes 7^3 / (1/25^4).
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/25^4 is 25^4.
Therefore, the equivalent expression is 7^3 * 25^4.
So the correct response is option A) 7^3 * 25^4.
The original expression is 7^3/25^(-4).
To apply the property of negative exponents, we can rewrite 25^(-4) as 1/25^(4). This means that 25^(-4) is equivalent to 1 divided by 25 raised to the power of 4.
So now the expression becomes 7^3 / (1/25^4).
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/25^4 is 25^4.
Therefore, the equivalent expression is 7^3 * 25^4.
So the correct response is option A) 7^3 * 25^4.