Question
9)
Use the properties of exponents to perform the following operation:
2^1/3⋅8^1/4
(1 point)
Responses
2^1/4
16^2/7
16^1/12
2^13/12
2^2/7
Use the properties of exponents to perform the following operation:
2^1/3⋅8^1/4
(1 point)
Responses
2^1/4
16^2/7
16^1/12
2^13/12
2^2/7
Answers
GPT 3.5
The correct answer is 2^(13/12).
To solve this, we can rewrite 8 as 2^3 and the expression becomes:
2^(1/3) * (2^3)^(1/4)
Using the property of exponents (a^m * a^n = a^(m+n)), we can simplify this to:
2^(1/3 + 3/4)
Finding a common denominator for 3 and 4, we get:
2^(4/12 + 9/12)
Simplifying further, we have:
2^(13/12)
To solve this, we can rewrite 8 as 2^3 and the expression becomes:
2^(1/3) * (2^3)^(1/4)
Using the property of exponents (a^m * a^n = a^(m+n)), we can simplify this to:
2^(1/3 + 3/4)
Finding a common denominator for 3 and 4, we get:
2^(4/12 + 9/12)
Simplifying further, we have:
2^(13/12)