How Do I do this step by step?

Question

Simplify each expression, if possible. Assume that all variables are unrestricted and use absolute value symbols when necessary.

(25y^2)^1/2

Answer 1

One property of taking the square root of a square number is the following:

|x| = sqrt(x^2)

In this case, ^(1/2) is equivalent to taking the square root.

(25y^2)^(1/2)

sqrt(25y^2)

And now, we can easily take the square root of this, since 25 is square and y^2 is square. As per the above property, our answer is

|5y|

Answer 2

(25y^2)^1/2

There's a rule in exponents that says
(x^m)^n= x^(mn)

25 = 5^2

So 25y^2 = (5^2)(y^2)

There's another rule in exponents that says
(x^m()y^m) = (xy)^m
So 5^2)(y^2)= (5y)^2

So you now have [(5y)^2]^(1/2)
Remember tat first rule?
(5y)^2]^(1/2)= (5y)^[(2)(1/2)]

Since (2)(1/2) = 1
(5y)^[(2)(1/2)] = (5y)^1 = 5y because x^1 = x

Unfortunately, there is another value that when multiplied by itself gives you 25y². How about -5y? (-5y)(-5y) also equals 25y². When faced with such a dilemma, it's safe to use the symbol "±" meaning "positive or negative" but often expressed verbally as "plus or minus.".

So your solution is actually ±5y

Because fractional exponents sometimes undo integer exponentiation, some people look on them as "inverse," or "opposite" operations. Not so. Same operation, just different numbers that have to behave according to the rules regarding exponents. It would be a good idea to learn them. I suspect that you'll be using them quite a bit.

Answer 3

(25y^2)^1/2
= (5^2 * y^2)^1/2
= (5^2)^1/2 * ( y^2)^1/2
= 5 * y = 5y

or power 1/2 means sqrt
(25y^2)^1/2 = sqrt ( 25y^2) = 5y

Answer 4

It is the square root and to the power of 1, therefore
25Y^2 ^ 1/2

+/- 5y

Answer 5

Just take the square root, as indicated. The square root of 25 is 5, and of y^2 is y. Since the result will be positive even if y is negative, the final result is |5y|.

Answer 6

(25y^2)^1/2=
sqrt(25y^2)=
sqrt(5*5*y*y)=
5y

*If you had taken the sqrt, the answer would be =+/- 5y but since the sqrt was given, it's just 5y

Answer 7

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Answer 8

(25y²)^1/2 = ± 5y

Still haven't hit the books? ☺


Doug

Answer 9

we are taking the squareroot of 25y^2.

we can do each part separatly.

sqrt(25) = +-5

sqrt(y^2) = +-y

so, squareroot of 25y^2 = +-5y and we are there.

Answer 10

(25y^2)^1/2
25^(1/2) * y^(2/2)
plus or minus 5y


Hope I didn't skip too many steps