Hey can someone explain this Alg. problem to me?

Question

Ok the deal is one-half times the fourth root of 32

1/2*[32^(1/4)]

Now I know the answer is the fourth root of two, but I have nooooo idea why....can anyone explain this to me?

Answer 1

1. any number ^ (1/x) power is the xth root of that number.
2. the fourth root of 32 is not even a rational number, so one has to use alternative means other than the calculator.
First, factor the number. 32 is 2 times 2 times 2 times 2 times 2. Since there are 4 2s in there, you can move it outside of the radical sign. You now have 1/2 times 2 times the fourth root of 2. Capische?

Answer 2

{32^(1/4)}=16^(1/4)x2^(1/4) = 2x2^(1/4) when you multiply this by 1/2, you get the answer 2^(1/4)
In general, any number to an exponent can be broken down into factors of that number, each to the same exponent.
Thus 32 is 16x2 and the fourth root of 16 is easily found as 2.
If AxB=C, then C^y=A^yxB^y.

Answer 3

You cannot multiply 1/2 by the power 32^(1/4)

You factorize 32 = 2^5

You write 1/2 as 2^(-1)

Now you have: 2^(-1)[(2^(5))]^(1/4)

You can multiply the exponents in [(2^(5))]^(1/4) and get

2^(5/4)

Now you have 2^(-1)2^(5/4) and you can add the exponents

-1 + 5/4 = 1/4

Finally you got 2^(-1)2^(5/4) = 2^(1/4)

Answer 4

Simplify the fourth root of 32 first.
Since 32 = 16 * 2 then fourth root of 32 = 2* fourth root of 2
Now your original is 1/2 * 2 * fourth root of 2
or fourth root of 2

Answer 5

32 = 2 * 2 * 2 * 2 * 2 = 2*(2^4)
Let x = (1/2) 32^(1/4)
Then:
Substitute 2*(2^4) for 32;
x = (1/2) ( 2*(2^4) )^(1/4)

Use (a*b)^c = (a^c) * (b^c):
x = (1/2) 2^(1/4) * (2^4)^(1/4)

Use (a^b)^c = a^(b*c):
x = (1/2) 2^(1/4) * 2^( 4 * (1/4) )

Multiply 4 * (1/4):
x = (1/2) 2^(1/4) * 2^1

Resequence factors:
x = 2^(1/4) * 2 * (1/2)

Multiply 2 * (1/2):
x = 2^(1/4)
x = 4th root of 2.

Answer 6

Take your calculator and find the value of 32 to the 0.25 power (THat is the 4 th root)

divide 32^.25 by 2 and that is the answer.

Answer 7

1 / 2 * ( 32 ) ^ (1/4)

32 can be written as ( 2 ) ^ 5

Also, 1/ 2 can be written as 2 ^ -1

So, [ 2 ^-1 ] * [ 2 ^ ( 5 / 4 ) ]

Using the exponent rules we have,

2 ^ [ -1 + 5/4 ] = 2 ^ (1/4) since, -1 + 5/4 = 1/4

So, the answer is 2 ^ (1/4).

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Answer 8

32=2*16=2*2^4

so: (2*2^4)^(1/4) = 2*2^(1/4) the 4th root of 2 to the 4th is 2
the 2 comes out of the radical leaving the 2^(1/4) inside...
1/2(2)=1 so the answer is just 2^(1/4)

Answer 9

1/2*[32^(1/4)]
= 1/2 (16*2)^1/4
= 1/2* 2 *(2^1/4)
= 2^1/4

Answer 10

1/2*[32^(1/4)]
= 1/2 (16*2)^1/4
= 1/2* 2 *(2^1/4)
= 2^1/4