5^9 * 5^(-13) can be simplified using the property of integer exponents that states: a^m * a^n = a^(m+n).
Therefore, the equivalent expression with only positive exponents is:
5^(9 + (-13)) = 5^(-4).
So, the equivalent expression with only positive exponents is 5^(-4).
Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
7 answers
Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
1/5^4
5^4
1/625
5^9/5^-13
1/5^4
5^4
1/625
5^9/5^-13
To find the equivalent expression with only positive exponents, we can apply the property of integer exponents that states: a^m * a^n = a^(m+n).
In this case, we have 5^9 * 5^(-13).
Using the property mentioned above, we add the exponents:
5^(9 + (-13)) = 5^(-4).
Therefore, the equivalent expression with only positive exponents is 5^(-4).
Among the options provided, the only one that matches 5^(-4) is 1/625.
So, the correct answer is 1/625.
In this case, we have 5^9 * 5^(-13).
Using the property mentioned above, we add the exponents:
5^(9 + (-13)) = 5^(-4).
Therefore, the equivalent expression with only positive exponents is 5^(-4).
Among the options provided, the only one that matches 5^(-4) is 1/625.
So, the correct answer is 1/625.
are you sure?
My apologies for the confusion. Upon further review, I made an error in my previous response.
To find an equivalent expression with only positive exponents for 5^9 * 5^-13, we can again apply the property of integer exponents, which states: a^m * a^n = a^(m+n).
Using this property, we can add the exponents:
5^9 * 5^-13 = 5^(9 + (-13)) = 5^-4.
Now, to convert 5^-4 into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^-n = 1/a^n.
Therefore, 5^-4 can be rewritten as 1/5^4.
So, the correct answer is 1/5^4. Thank you for pointing out the mistake.
To find an equivalent expression with only positive exponents for 5^9 * 5^-13, we can again apply the property of integer exponents, which states: a^m * a^n = a^(m+n).
Using this property, we can add the exponents:
5^9 * 5^-13 = 5^(9 + (-13)) = 5^-4.
Now, to convert 5^-4 into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^-n = 1/a^n.
Therefore, 5^-4 can be rewritten as 1/5^4.
So, the correct answer is 1/5^4. Thank you for pointing out the mistake.
positive?
Apologies for the confusion earlier. Let's revisit the problem.
We have the expression 5^9 * 5^(-13).
To simplify this expression using the property of integer exponents, we can add the exponents:
5^9 * 5^(-13) = 5^(9 + (-13)) = 5^(-4).
To convert 5^(-4) into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^(-n) = 1/a^n.
Therefore, 5^(-4) can be rewritten as 1/5^4.
So, the correct answer is 1/5^4. Thank you for pointing out the error in my previous response.
We have the expression 5^9 * 5^(-13).
To simplify this expression using the property of integer exponents, we can add the exponents:
5^9 * 5^(-13) = 5^(9 + (-13)) = 5^(-4).
To convert 5^(-4) into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^(-n) = 1/a^n.
Therefore, 5^(-4) can be rewritten as 1/5^4.
So, the correct answer is 1/5^4. Thank you for pointing out the error in my previous response.