Apply All Exponent Rules Quick Check

Question

1 of 51 of 5 Items
Question
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 point)
Responses

5^4
5 superscript 4 baseline

1/5^22
Start Fraction 1 over 5 superscript 22 baseline end fraction

5^9/5^−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction

1/5^4

Answer 1

To simplify the expression \( 5^9 \cdot 5^{-13} \) using the properties of exponents, we can use the rule that states \( a^m \cdot a^n = a^{m+n} \).

So, we calculate:

\[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{-4} \]

Next, we need to express this with only positive exponents. We can change \( 5^{-4} \) to positive exponent form by using the property \( a^{-n} = \frac{1}{a^n} \):

\[ 5^{-4} = \frac{1}{5^4} \]

Now, looking at your options, we see that the equivalent expression with only positive exponents is:

\[ 1/5^4 \]

Thus, the correct response is 1/5^4.