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
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).
To find the equivalent form using the product rule of exponents for the expression 1/3 raised to the power of 6, we can multiply the exponents.
Let's break it down step-by-step:
Step 1: Rewrite the expression using fractional exponents.
1/3 with a small six on top can be written as 3^(-6).
Step 2: Apply the product rule of exponents.
The product rule states that when multiplying two exponential expressions with the same base, you add the exponents.
So, we have:
3^(-6) × 1/3 with a small tree on top of the one-third
Step 3: Rewrite the second expression using fractional exponents.
1/3 with a small tree on top can be written as 3^(-1).
Step 4: Multiply the two expressions.
Using the product rule, we add the exponents:
3^(-6) × 3^(-1) = 3^(-6 - 1) = 3^(-7)
Therefore, an equivalent form of 1/3 with a small six on top of the one-third multiplied by 1/3 with a small tree on top of the one-third is 3^(-7).
To rewrite the expression using the product rule of exponents, we need to multiply the two fractions together. Let's break it down step by step:
First, we have 1/3 with a small six on top of the "one-third," which can be written as:
(1/3)⁶
Next, we have the expression 1/3 with a small tree on top of the "one-third," which can be written as:
(1/3)³
To find an equivalent form of the original expression, we need to multiply these two expressions together:
(1/3)⁶ × (1/3)³
When multiplying two numbers with the same base (in this case, 1/3), we can add the exponents:
(1/3)⁶ × (1/3)³ = (1/3)⁶+³ = (1/3)⁹
Therefore, an equivalent form of the original expression is:
(1/3)⁹, which is read as "one-third to the power of nine."