Question
Using the product rule of exponents, what is an equivalent form of 1/3 with a small six on top of the one 3rd×1/3 with a small tree on top of the one third
Answers
Answered by
GPT 3.5
To find an equivalent form for the given expression, we can simplify using the product rule of exponents.
The product rule states that when multiplying exponential expressions with the same base, we add their exponents.
Let's break down the given expression:
1/3 with a small six on top of the one third can be represented as (1/3)^(1/6).
1/3 with a small tree on top of the one third can be represented as (1/3)^(1/3).
Now, we can simplify the expression by taking the product of these two expressions:
(1/3)^(1/6) * (1/3)^(1/3)
Applying the product rule of exponents, we add the exponents:
(1/3)^((1/6) + (1/3))
To find a common denominator for the fractional exponents, we can write (1/6) as (1/6) * (2/2) = 2/12.
(1/3)^((2/12) + (4/12))
(1/3)^(6/12) [Adding the fractions]
(1/3)^(1/2) [Simplifying the fraction]
Therefore, an equivalent form of the given expression (1/3 with a small six on top of the one third × 1/3 with a small tree on top of the one third) using the product rule of exponents is (1/3)^(1/2).
The product rule states that when multiplying exponential expressions with the same base, we add their exponents.
Let's break down the given expression:
1/3 with a small six on top of the one third can be represented as (1/3)^(1/6).
1/3 with a small tree on top of the one third can be represented as (1/3)^(1/3).
Now, we can simplify the expression by taking the product of these two expressions:
(1/3)^(1/6) * (1/3)^(1/3)
Applying the product rule of exponents, we add the exponents:
(1/3)^((1/6) + (1/3))
To find a common denominator for the fractional exponents, we can write (1/6) as (1/6) * (2/2) = 2/12.
(1/3)^((2/12) + (4/12))
(1/3)^(6/12) [Adding the fractions]
(1/3)^(1/2) [Simplifying the fraction]
Therefore, an equivalent form of the given expression (1/3 with a small six on top of the one third × 1/3 with a small tree on top of the one third) using the product rule of exponents is (1/3)^(1/2).