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
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
1625
Start Fraction 1 over 625 end fraction
595−13
595^(-13)
To find an equivalent expression with only positive exponents, we can apply the properties of integer exponents.
The given expression is 59⋅5−13.
First, let's use the property of negative exponents: a^(-n) = 1/a^n.
Applying this property to 5^(-13), we get 1/5^13.
So, the expression becomes 59 * (1/5^13).
Next, let's simplify 1/5^13 using the property of negative exponents again: 1/5^13 = 5^(-13).
So, the expression becomes 59 * 5^(-13).
Now, using the property of multiplying with the same base: a^n * a^m = a^(n+m), we can rewrite the expression as 59 * 5^(-13) = 5^(4-13).
Simplifying 5^(4-13), we get 5^(-9).
Now, using the property of negative exponents again, we have 5^(-9) = 1/5^9.
Therefore, the equivalent expression with only positive exponents is 1/5^9.
So, the correct option is: Start Fraction 1 over 5^4 End Fraction.
To find an equivalent expression with only positive exponents, let's break down the given expression step by step and apply the properties of integer exponents:
Expression: 59⋅5−13
Step 1: Simplify the base with a negative exponent by using the rule a^(-n) = 1/a^n.
59 ⋅ 5^(-13) = 59 ⋅ (1/5^13)
Step 2: Simplify the expression 1/5^13 by using the rule (a/b)^n = a^n/b^n.
59 ⋅ (1/5^13) = 59/5^13
Step 3: Simplify the expression 59/5^13 by using the rule a^n / a^m = a^(n-m).
59/5^13 = 59/(5^(13-0)) = 59/5^13
So, the equivalent expression with only positive exponents is 59/5^13.