Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3
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Explanation:
There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative.
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A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative
sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative
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If we allow m to be negative, then the final result would be either |m^3| or |m|^3.
The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.
Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2
Answer:
24 days
Step-by-step explanation:
To determine the number of days until they both work out at the gym on the same day again,
Find the lowest common multiples of 4 days and 6 days
Clint (4 days) = 8, 12, 16, 20, 24, 28, 32
Max (6 days) = 12, 18, 24, 30, 36, 42
The lowest common multiple of ,4 days and 6 days is 24 days
Therefore, the number of days until they both work out at the gym on the same day again is 24 days
What are the numbers given?
Answer: I think it is 1572 sq feet
Step-by-step explanation:
Lxwxh
14x13x9=1638
Window is 4x4.5=18
Door 1 is8x3=24
Door 2 8x3=24
Since the doors and window are not included in what was painted you need to subtract those totals from the room.
So, 1638-18=1620
1620-48(two doors)=1572 sq feet
Answer:
x-intercept is (-4,0) and the y-intercept is (0,-2
Step-by-step explanation:
There are 2 ways to find the y-intercept. One way is to put the equation in slope-intercept form. However, there is a more efficient way as well.
Another way to do it is to plug 0 in for x and y. The x-intercept will have the coordinate of (x,0). So to find the x-intercept you can plug in 0 for y and solve for x. To find the y-intercept do the opposite and plug 0 in for x.
So, first, plug 0 in for y
- x+2(0)=-4
- x+0=-4
- x=-4
Then plug in 0 for x
- 0+2y=-4
- 2y=-4
- y=-2
Therefore, the x-intercept is (-4,0) and the y-intercept is (0,-2).
