simplify r2/3r-1/r-1/2
r2/3r-1/r-1/2 =
Move the negative exponent in the numerator to the denominator and move the negative exponent in the denominator to the numerator.
r2/3r1/2/r1 =
Now combine the exponents by adding them. You must have a common denominator to combine 2/3 and 1/2 So that will be 4/6 and 3/6. Can you take it from here?
yes thank you...
To simplify the given expression, we can use the rules of exponents.
Let's break down the expression step by step:
Step 1: Combine the exponents of the same base by using the exponent rule for multiplication.
- Multiplication Rule: When you multiply two numbers with the same base, you add the exponents.
In this case, we have r^(2/3) * r^(-1) = r^(2/3 - 1).
Step 2: Simplify the exponent using arithmetic operations.
- Subtracting fractions: To subtract fractions with the same denominator, we can simply subtract the numerators.
Applying this rule, our exponent simplifies to r^(2/3 - 3/3) = r^(-1/3).
Step 3: Apply the division rule for exponents.
- Division rule: When you divide two numbers with the same base, you subtract the exponents.
Therefore, r^(-1/3) / r^(-1/2) = r^(-1/3 - -1/2) = r^(-1/3 + 1/2).
Step 4: Simplify the resulting exponent.
- Adding fractions: To add fractions with different denominators, we need to find a common denominator.
The common denominator of 3 and 2 is 6. Therefore, our exponent simplifies to r^(-2/6 + 3/6) = r^(1/6).
So the simplified form of r^(2/3) * r^(-1) / r^(-1/2) is r^(1/6).