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
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
54
5 superscript 4 baseline
595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1625
595−13
Which property of exponents was used to generate the equivalent expression 314 from 353−9?(1 point)
Responses
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Product Rule of Exponents
only the Product Rule of Exponents
only the Power Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
only the Power Rule of Exponents
To find an equivalent expression with only positive exponents for 59⋅5−13, we can apply the property of integer exponents which states that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
So, 59⋅5−13 is equivalent to 59⋅1/5^13.
This can be simplified further as 59 divided by 5^13.
Hence, the correct answer is:
Start Fraction 59 over 5 superscript 13 baseline end fraction.