(cube root of 5) * sqrt(5)
--------------------------------- = ?
(cube root of 5^5)
This becomes easier if we switch to fractional exponents:
5^(1/3) * 5^(1/2) 5^(1/3 + 1/2) 5^(5/6)
------------------------ = --------------------- = ------------- = 5^[5/6 - 5/3]
[ 5^5 ]^(1/3) 5^(5/3) 5^(5/3)
Note that 5/6 - 5/3 = 5/6 - 10/6 = -5/6.
1
Thus, 5^[5/6 - 5/3] = 5^(-5/6) = --------------
5^(5/6)
That's the correct answer. But if you want to remove the fractional exponent from the denominator, do this:
1 5^(1/6) 5^(1/6)
---------- * ------------- = -------------- (ANSWER)
5^(5/6) 5^(1/6) 5
The absolute value of a real number a is a when a≥0, or -a when a<0. The absolute value of -6 is 6. The absolute value of 4 is 4.
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Answer:
x = 12, x = 7
Step-by-step explanation:
The 2 legs of the triangle are congruent, both 2x + 7, then
2x + 7 + 2x + 7 + x + 11 = 85 ← equation for perimeter
5x + 25 = 85 ( subtract 25 from both sides )
5x = 60 ( divide both sides by 5 )
x = 12
-----------------------------------------------------------
Opposite sides are congruent, then
2(2x) + 2(5x + 3) = 104 ← distribute and simplify both sides
4x + 10x + 6 = 104
14x + 6 = 104 ( subtract 6 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
The way you can get this answer you can use the calculater
For question 1, the largest value would be 1 and the smallest value would be -1. A, B, and C are either all 1 or two is negative and one is positive, either way the number is 1 and it's opposite. 1^2 is 1, 1^3 is 1, 1^4 is 1. The product is 1. -1^2 is -1, -1^3 is -1, -1^4 is -1. The product is -1. Now the difference. 1 - (-1), which is 1 + 1, the answer is [D) 2]
