(r^-3s^1/3)^6/r^7s^3/2
Did you mean it the way you typed it, or did you mean:
(r^-3s^1/3)^6/(r^7s^3/2)
btw, what is the question?
Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.
And, yes, the way you wrote it. I forgot the parenthesis on the bottom.
To simplify the expression (r^-3s^1/3)^6/r^7s^3/2, let's break it down step by step:
Step 1: Simplify the numerator.
The numerator is (r^-3s^1/3)^6. To simplify this, we can apply the exponent rule which states that when raising a power to another power, you multiply the exponents.
So, (r^-3s^1/3)^6 becomes r^-18s^2.
Step 2: Simplify the denominator.
The denominator is r^7s^3/2. In this expression, we have r^7 and s^3/2. To simplify this, we need to apply the exponent rules.
For the r^7, it remains as it is since there is no other exponent to apply.
For the s^3/2, we can rewrite it as the square root of s^3. The exponent 3/2 means taking the square root of s and then raising it to the power of 3.
So, s^3/2 becomes √s^3^3, which is equal to √s^9.
Step 3: Combine numerator and denominator.
Now that we have simplified the numerator and denominator separately, we can combine them.
So the final expression is (r^-18s^2)/(r^7√s^9).
To simplify it further, we can use another exponent rule that says when you divide powers with the same base, you subtract the exponents.
So, r^-18/r^7 becomes r^-18-7, which is r^-25.
Also, for s^2/√s^9, we can simplify it by applying the exponent rule. The square root of s^9 is s^(9/2), so the expression becomes s^2/s^(9/2), and using the rule for division of powers with the same base, we subtract the exponents, giving us s^2-9/2, which is s^(-5/2).
So, the final simplified form of the expression is r^-25s^(-5/2).