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
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.
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.
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.
To convert the expression 7^3/25^(-4) into an equivalent expression with only positive exponents, we can use the Property of Negative Integer Exponents, which states that a^(-n) is equal to 1/a^n.
So, in this case, 25^(-4) can be rewritten as 1/25^4.
Therefore, the expression 7^3/25^(-4) is equivalent to 7^3 * (1/25^4).
Hence, the correct answer is 7^3 * 25^4.
To simplify the given expression and rewrite it with only positive exponents, we can use the Property of Negative Integer Exponents, which states that for any non-zero value of x, x^(-n) can be rewritten as 1/(x^n).
For the expression 7^3/25^(-4), we can apply this property to the denominator.
First, we rewrite 25^(-4) as 1/(25^4) using the Property of Negative Integer Exponents.
So, the expression becomes:
7^3 / (1/(25^4))
Next, we multiply the numerator and denominator by the reciprocal of the denominator. In this case, we multiply by 25^4.
This results in:
(7^3)(25^4) / 1
So, the equivalent expression with only positive exponents, generated by applying the Property of Negative Integer Exponents, is 7^3 * 25^4.
Therefore, the correct answer is the option: 7^3 * 25^4