Math square root problem

[andyjl]

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The fourth root of x^3 times the square root of x equals 32. What is x?

please help.

answer is x = 16

 

[domonas]

The fourth root of x^3 times the square root of x equals 32. What is x?

please help.

answer is x = 16

Hmm, 4th root of x^3 = x^(3/4)
square root of x = x^(1/2)

multiply those two together, you get x^(5/4) = 32
---remember, exponents are added, so 3/4 + 1/2 (or 2/4) = 5/4

another way to break down 5/4 is 1/4 + 4/4 (which is 1/4 +1)
which means
(x^1/4)(x^4/4) = 32
x^4/4 = x
(x^1/4)(x)=32

16 is right.

 

[ATLATLATL]

i c how ur getting the 5/4 but how are you getting 16?
are u subracting 5/4 from 32?

 

[jdmsamurai]

x^(5/4) = 32
x^(5/4) = 2^5

now here comes the tricky but easy part 4th everything so it would be
(x^(5/4))^4 = (2^5)^4
x^5 = 2^20

now fifth root everything
x = 2^4
x = 16

ta da...magic

 

[cdmOMR]

Another way to look at it is once you get to 32^(4/5) you can seperate it into (32^1/5)^4....32^1/5 should pop out in your head to = 2, since 2^5=32...so its simply 2^4=16

 

[Mila]

X^(5/4) = 32
so....
X = 32^(4/5)
.....which is really just the fifth root of 32^4

fifth root of 32 is 2 .... so we have 2^4... which is 16.