Answer:
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Step-by-step explanation:
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:
Step-by-step explanation:
Your gonna subtract the cost of the pair earrings from the total. 260-15=245, then you will divide 245 by 7. 245/7=35. So each bracelet cost's 35 each.
The intersection of the two red rays forms a set of vertical angle pairs. In such a pair, angles opposite one another have the same measure, so the angle opposite the one labeled 93 degrees also has measure 93 degrees.
The red ray on the right together with the black ray pointing directly to the right form a pair of supplementary angles, whose measures add up to 180 degrees. This means the angle adjacent to the one labeled 128 degrees has measure 180 - 128 degrees.
In any triangle, the interior angles' measures add up to 180 degrees. So we have
? + 93 + (180 - 128) = 180
? + 93 - 128 = 0
? = 128 - 93
? = 35