Radical Expressions?

Question

I'm stumped on these, I've been able to do some, but the exponent on the outside of the square root is really throwing me off, any help is greatly appriciated. I hope it's readable, typing it out online is rough :), I've included answers for the ones that I was able to work through, although not all of them are complete.

√ = Square Root
^ = Exponent
/ = Numerator/Demoninator

Simplify. Assume that variables can represent any real number.

1) ^3√-8 / x^12
A) -2 / x^3

2) ^5√x^7y^2

3) √25x^6 / 16y^2
A) 5x^3 / 4y

4) (^3√6x)(^3√2y)
A) 2√x/

5) ^5√x^6y^4 / ^5√x^2y^3

6) (^4√xy^2)(√xy)

7) ^5√a^3 / ^4√a^2

8) 7√2 - 3√2
A) 4√2

9) (3 + √x)(7 - 5√x)

10) (√-4)(√-81)
A) 18

11) √48
A) √4√8

12) √36a^2
A) 6a

13) √x^2 - 12x + 36
A) | x - 6 |

14) Rewrite using radical notation: (2ab)^4/5
A) (^5√2ab)^4

15) Rewrite using exponential notation: √6x^2y

16) f(x) = √12 - 3x, determine the domain of f.

17) f(x) = x^2, find f(2 + √6)

18) Rationalize the denominator: √6 / 5 - √5

Answer 1

1) ^3√-8 / x^12

I write this as
(-8/x^12)^3 = (-8)^3 * (1 / x^12 ) ^ 3

next i use this

1/x^n = x^(-n)
(x^p) ^ n = x^(p*n)
^p√ x = x^(1/p)

that is all..

1) ^3√-8 / x^12
A) -2 / x^3 <== is wrong correct==> -2 / x^(12/3)

Answer 2

ok, right here is going no longer something: area a million: a million. 3sqrtx * 3 sqrtx = 9x (sqrt * sqrt eliminates the sqrt) 2. sqrt t * sqrt t = t 3. 3 sqrt R / 3 sqrt x = sqrt R / sqrt x area 2: a million. 4 sqrt x^2 = 4x (a million/2*2 = a million) 2. sqrt t = t^a million/2 3. 4 sqrt x^7 (reminiscent of a million: a million/2 * 7 = 7/2) so 4x^7/2 4. a million/ 5sqrt x^2 = a million/5x area 3: a million. x^2 / y^-3 = x^2 y^3 (you place a a million over y then convey it up) 2. x^3 y^-5 = x^3/y^5 3. x^2y^-4z^4 = x^2z^4 / y^4 4. x^2 / y^-a million/2 = x^2 y^a million/2 5. x^2 y^3 t^-4 z^-6 w = x^2 y^3 w / t^4 z^6 pass unfavourable exponents to the denominator desire this helps.

Answer 3

The "exponent" in front of the radical is actually not an exponent at all. By convention, a radical with no number preceding it is a square root, but if a number exists, it refers to a root other than 2.

Answer 4

jeez i dont understand your terminology and its 18 problems, do your homework for once.