The question is the expression (m^2/m^1/3)^-1/2 is equivalent to:
I did
(m^5/3)^1/2
m^-5/6
1/m^5/6
so my answer is 1/ the 6th root m^5
sorry I don't know how to print a square root symbol.
Is this correct? Thank you for checking my work
looks good
Well, well, well, look who's back with some mathematical mischief! Let's dive into it, my friend.
The expression you've been given is (m^2/m^(1/3))^(-1/2), and you've put forward a few options. Let's see which one tickles our funny bone!
Option 1: (m^(5/3))^(1/2) - It seems like you're applying the rule that when you raise something to one exponent and then raise that result to another exponent, you simply multiply the exponents. However, this is not applicable here. Nice try, though!
Option 2: m^(-5/6) - You seem to be on the right track this time! Remember, when a negative exponent is applied to a term, you can move it to the denominator and change the sign of the exponent. Keep going!
Option 3: 1/m^(5/6) - Ah, you've moved the term with the negative exponent to the denominator. Great job! But wait, it seems like the exponent isn't quite correct.
After evaluating the expression thoroughly, the correct option seems to be: 1/m^(5/6).
Fantastic effort, my friend, but let me tell you, mathematics can be a real circus sometimes! Keep practicing, and you'll be cracking mathematical jokes in no time.
To check if your answer is correct, we can simplify the given expression step by step:
Given expression: (m^2/m^(1/3))^(-1/2)
Step 1: Simplify the exponent inside the parentheses.
m^2/m^(1/3) = m^(2 - 1/3) = m^(5/3)
Step 2: Take the reciprocal of the expression inside parentheses.
(m^(5/3))^(-1/2) = 1/(m^(5/3))^(1/2)
Step 3: Apply the power of a power rule, which states that (a^m)^n = a^(m * n).
1/(m^(5/3))^(1/2) = 1/m^((5/3) * (1/2)) = 1/m^(5/6)
So, your answer of 1/m^(5/6) is correct.
To determine if your answer is correct, let's simplify the expression step by step and compare it with your answer.
Starting with the expression:
(m^2/m^(1/3))^(-1/2)
First, we can simplify the numerator and denominator separately:
(m^2) / (m^(1/3))
To combine the terms in the denominator, we subtract the exponents:
m^(2 - 1/3)
Next, we combine the numerator and denominator by subtracting the exponents:
m^(2 - 1/3) = m^(5/3)
Finally, we raise the expression to the power of (-1/2):
(m^(5/3))^(-1/2)
When raising a power to another power, we multiply the exponents:
m^(5/3 * -1/2) = m^(-5/6)
So, the simplified expression is m^(-5/6).
Comparing this result with your answer, we can see that they are the same. Therefore, your answer of 1/ the 6th root of m^5 is correct.
Great job!