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?
Responses
5^4
1/5^4
1/625
5^9/5^−13
To simplify the expression and apply the properties of integer exponents, we can add the exponents when multiplying and subtract the exponents when dividing.
In this case, when we multiply two powers with the same base, we add the exponents. So, 5^9 * 5^(-13) simplifies to 5^(9+(-13)), which is equal to 5^(-4).
When we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent. So, 5^(-4) is equivalent to 1/5^4.
Therefore, the equivalent expression with positive exponents is 1/5^4.
So, the correct answer is 1/5^4.
To simplify the expression 5^9⋅5^−13 using the Properties of Integer Exponents, we can add the exponents of the same base (in this case, 5).
So, 5^9⋅5^−13 can be rewritten as 5^(9 + (-13)).
Since adding a negative number is the same as subtracting that number, we can simplify further:
5^(9 + (-13)) = 5^(9 - 13)
= 5^(-4)
Therefore, the equivalent expression with only positive exponents is 1/5^4.
So, the correct option is 1/5^4.
To find an equivalent expression with only positive exponents, we can apply the properties of integer exponents.
The property we can use is the Product of Powers rule, which states that when you multiply two exponent expressions with the same base, you add the exponents.
So, for the given expression 5^9⋅5^−13, we can add the exponents:
5^9⋅5^−13 = 5^(9 + (-13))
Simplifying the exponent, we have:
= 5^(-4)
Now, to convert the negative exponent to a positive exponent, we can use the property that a negative exponent is equal to the reciprocal of the positive exponent. So,
5^(-4) = 1/5^4
Therefore, the equivalent expression with only positive exponents is 1/5^4.