How do I rewrite this as a radical expression?
(3 2/3) 1/6
(32/3)1/6
(xA)B = xAB so we multiply the exponents
3(2/3)(1/6)
3(2/18)
31/9
x1/y = y√x
31/9 = 9√3
Answers
(32/3)1/6
•(xA)B = xAB so we multiply the exponents
3(2/3)(1/6)
3(2/18)
31/9
•x1/y = y√x
31/9 = 9√3
The answer is 9√3
Thank you both so much I think I got it now :)
To rewrite the given expression as a radical expression, we need to convert the mixed number and the fraction into improper fractions. Then, we can write it as a radical expression. Here's a step-by-step explanation:
Step 1: Convert the mixed number into an improper fraction.
To convert 3 2/3 into an improper fraction, multiply the whole number (3) by the denominator of the fraction (3) and add the numerator (2). This will give you the numerator of the improper fraction. Keep the denominator the same. So, we have:
3 * 3 + 2 = 11
----------------
3
Step 2: Convert the fraction 1/6 into an improper fraction.
Since the numerator (1) is already smaller than the denominator (6), we can directly write it as an improper fraction. So, we have:
1
---
6
Step 3: Multiply the two improper fractions.
To multiply the improper fractions, multiply the numerators together and the denominators together. So, we have:
11 * 1 = 11
-------
3 * 6 = 18
Step 4: Rewrite the result as a radical expression.
To rewrite 11/18 as a radical expression, notice that the denominator (18) is divisible by a perfect square. In this case, it's divisible by 9, which is a perfect square. So, we can write the expression as follows:
11/18 = (11/9)(1/2)
Now, we can rewrite the expression as a radical expression:
(11/9)(1/2) = √11/√9 (where √ represents the square root)
Thus, the given expression (3 2/3) 1/6 can be written as √11/√9.