Which of the following is an equivalent expression to 5 exponent 9 ⋅ 5 exponent −13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/625
5 exponent 9/5 exponent −13
1/5 exponent 4
5 exponent 4
The correct answer is 5 exponent 4. This is equivalent to 5 exponent 9 ⋅ 5 exponent −13 because when you multiply two exponential expressions with the same base, you add the exponents. In this case, 9 + (-13) is equal to 4.
If you have time can you put the correct answers in please, The Bot is sometimes incorrect because one time for math I got a 1 out of 5 so, please make sure you or anyone who sees this comment please put the right answers in after you are done with your assignment because we need to know what the right answers are, not what the Bot decides to say.
I apologize for any confusion or incorrect answers provided by the bot. Here are the correct answers to the question:
The equivalent expression to 5 exponent 9 ⋅ 5 exponent −13 with only positive exponents is 5 exponent 4.
To find an equivalent expression with only positive exponents, we can use the property of exponents that states: When we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent.
The given expression is 5^9 * 5^-13.
To rewrite this expression with only positive exponents, we can apply the property mentioned above.
5^(-13) can be rewritten as 1/(5^13).
Therefore, the equivalent expression with only positive exponents is 5^9 * (1/5^13).
Simplifying this expression further, we can combine the terms with the same base and subtract the exponents:
= 5^(9-13)
= 5^-4
So, the equivalent expression with only positive exponents is 5^(-4).
Therefore, the correct response is: 5 exponent 4.
To find an equivalent expression with only positive exponents, we can apply the Property of Integer Exponents which states that a^(-n) is equal to 1/a^n.
In the given expression, 5 exponent -13 has a negative exponent. Applying the property, we can rewrite it as 1/5 exponent 13.
Now we have 5 exponent 9 ⋅ 1/5 exponent 13. To multiply these expressions together, we can add their exponents since they have the same base (which is 5).
So, 5 exponent 9 ⋅ 1/5 exponent 13 becomes 5 exponent (9 + 13) = 5 exponent 22.
Therefore, an equivalent expression with only positive exponents would be 5 exponent 22.
So, the correct answer is: 5 exponent 4