Could you PLEASE help me on these algebra 2 questions?

Question

Hi, I'm having a bit of trouble on my homework....on algebra 2...The questions are:

1.
(i don't have the symbols on this keyboard so i'll write it in words)
simplify: the 3rd root of 40 mulitiplied by 4 times the 3rd root of 5. like= ^3radical40 X(times) 4^3radical5

X=multiply
2. simplify: (5^4/5 X 5^4/5) ^-10

3. simplify: the 3rd root of 2 divided by the 3rd root of 54.

4. simply: the square root of 64x^12

5. simplify: (7^3/4)^-2/9

6. write the expression in simplest form: the 3rd root (aka cubed root) of 1/5.

7. Let f(x)=4-x^2 and g(x)=2-x. find f(x) divided by g(x).

8. Let f(x)=16-x^2 and g(x)=4-x. Find (f X g)(x). (again X means multiply.)

9. Let f(x)=4-x^2 and g(x)=2-x. Find f(g(x))

10. Solve the equation and check for extraneous solutions:

the sq. root of x^2 + 5 = 3-x


OK that's the ones i'm having trouble on the most....... i KNOW it's a lot, but if you could help me with any one of them, it would be so great.

Thank you! =)

Answer 1

the key is to simplify under the radicals

1) cbrt(40) * 4*cbrt(5) =
cbrt(8*5) * 4*cbrt(5) =
cbrt(8) * cbrt(5) * 4*cbrt(5) =
2 * 4 * cbrt(5) * cbrt(5) =
8 * cbrt(25)

3) cbrt(2)/cbrt(54) =
cbrt(2)/cbrt(27*2) =
cbrt(2)/cbrt(27)*cbrt(2) =
cbrt(2)/3*cbrt(2) =
(cbrt(2)s cancel out) =
3

most of the others can be done like that

Answer 2

2){ [5^4/5] x [5^4/5] }^-10
= {[5^3] x [5^3]}^-10
={[5^3]x[5^3]}^-10
=5^-60
=1/5^-60
3){2/54}^1/3
={1/27}^1/3
=1/3
4){64x^12}^1/2
={[8x8]x[x^6][x^6]}^1/2
=8x^6
5){[7^3/4]}^-2/9
={1/[7^3/4]^2/9}
={1/[7^6/36]}
={1/7^1/6]}
={7^-1/6}
7)f(x)=[4-x^2]/[2-x]
=[2-x] [2+x] / [2-x]
=2+x
8)f(x)=16-x^2
g(x)=4-x
f(x) x g(x) =16-x^2 x 4-x
=64-4x^2-16x+x^3
9)f{g(x)}=4-[2-x]^2
=4-4-x^2+4x
= -x^2+4x
10){x^2+5}^1/2=3-x
x^2+5=9+x^2-6x
6x=9-5
6x=6
x=1

Answer 3

I don understand what r u writting but i'll try to answer some of it

8. fg(x) = f[g(x)]
fg(x) = f(4 - x)
= 16 - (4 - x)^2
= 16 - (4 - x)(4 - x)
= 16 - (16 - 8x + x^2)
= x^2 - 8x

9. fg(x) = f[g(x)]
= f(2 - x)
= 4 - (2 - x)^2
= 4 - (2 - x)(2 - x)
= 4 - (4 - 4x + x^2)
= x^2 - 4x