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:
44
Step-by-step explanation:
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
First we need to do the work inside the parenthesis that are in the boxed parenthesis
3 + 1 = 4
4 * 5 = 20
Now we multiply
20 * 2 = 40
Now we add
40 + 4 = 44
Best Of Luck,
- I.A. -
Distance = speed * time
d = 40(2)
d = 80 miles
Answer:
4, 4√3
Step-by-step explanation:
In a 30-60-90 triangle:
The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4
The longer leg is √3 times the shorter leg: 4*√3 = 4√3
Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64
