Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
54
5 superscript 4 baseline
595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
1625
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
To find an equivalent expression with only positive exponents, we can apply the Property of Integer Exponents which states that a^m /a^n = a^(m-n).
Therefore, the equivalent expression to 59⋅5−13 with only positive exponents is:
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
To find an equivalent expression to 59⋅5−13 with only positive exponents by applying the properties of integer exponents, we can use the property that a negative exponent is equivalent to the reciprocal of the positive exponent.
So, let's express the given expression using positive exponents:
59⋅5^(-13) can be rewritten as 59⋅(1/5^(13))
Now, using the property mentioned earlier, we can rewrite 1/5^(13) as 5^(-13).
Putting it all together, the equivalent expression with only positive exponents is:
59⋅5^(-13) = 59⋅5^(-13) = 59⋅5^(13)