I needs help with this problem. Please red carefully its tough to write it out.?

Question

Ok i need help with this problem but its hard to type out.......

Simplify

This is going to be the square root sign with a little 3 on left side and inside the root is 16a^3 b^4 - (minus) another root sign with the little 3 on the left and inside this root is 54a^3 b^4

Answer 1

The little three means you are taking the cubed root of what is inside.

The cubed root of 16 a^3b^4 is: (break into multiple steps)

cubed root of 16 is 2 cubed root of 2
(b/c 16 = 2*2*2*2 ; three of the twos can be grouped together and pulled out of cubed root creating one 2 in front of the square root.)
cubed root of a^3 is a (remember it is now outside of cubed root)
cubed root of b^4 is b cubed root of b
(b/c b^4 = b*b*b*b ; three of the b's can be grouped together and pulled out of cubed root.)

so for the before the subtraction sign you have:
2ab cubed root 2b


The cubed root of 54 a^3b^4 is: (break into multiple steps)

cubed root of 16 is 3 cubed root of 2
(b/c 54 = 3*3*3*2 ; three of the threes can be grouped together and pulled out of cubed root.)
The a and b are same as listed above

so for the after the subtraction sign you have:
3ab cubed root 2b


Now you have:
2ab cubed root 2b - 3ab cubed root 2b

Because they have the same numbers in the cube they can be combined.
2ab cubed root 2b - 3abcubed root 2b is -1abcubed root 2b



the answer:
-ab cubed root 2b


If you don't understand how to know what the cubed root of something is let me know and I will explain further.

Hope this helps!

Answer 2

first : as you write for example square root of "a" like " a^1/2",
you can write the square root of "a" with that small 3 on the left like "a^1/3" , and this is called " third root of a". same thing if you have 4, 5 etc. on the left over the sign of square root.
{ (16a^3 b^4) ^1/3 } - { (54a^3 b^4) ^1/3 }
={ (16^1/3) (a^3)^1/3 (b^4)^1/3 } - { (54)^1/3 (a^3)^1/3 (b^4)^1/3 }
= { (2*8)^1/3 a (b^4)^1/3 } - { (2*27)^1/3 a (b^4)^1/3 }
= { (2^1/3) (2^3)^1/3 a (b^4)^1/3 } - { (2^1/3) (3^3)^1/3 a (b^4)^1/3 }
= { (2^1/3) 2 a (b^4)^1/3 } - { (2^1/3) 3 a (b^4)^1/3 }
= (2^1/3) (b^4)^1/3 (2a - 3a)
= - a { (2^1/3) (b^4)^1/3 }
= - a { (2b^4)^1/3 }
p.s. " * " means multiplied by. As when you have square root of "a^2" it equals with "a", so it is when you have (a^3)^1/3 it equals with "a". etc. with 4, 5 .....

Answer 3

the little three thing with a root is the cube root... I will use the symbol "cbrt(...)" to denote cube root.

cbrt(16a^3b^4)-cbrt(54a^3b^4)
you can simplify the a^3 because the cube root of a^3 is a, and you can take out b^3 of the b^4.

so ab*cbrt(16b)-ab*cbrt(54b)

54=27*2 and 16=8*2 so you can simplify those because 27 is 3^3 and 8 is 2^3...

so 3ab*cbrt(2b)-2ab*cbrt(3b)

That is as simple as it gets

Answer 4

I think you mean the "little 3" is in the V portion of the radical sign meaning take the cube root of what's under the radical sign. The other possible interpretation is that the 3 is multiplying the entire radical. So my interpretation is that you have a cuberoot within a cuberoot, and not simply the difference between to cube roots.

cuberoot[16a^3b^4 - cuberoot(54a^3b^4)]
=cuberoot[2b(2ab)^3 -cuberoot(2b(3ab)^3]
=cuberoot [2b(2ab)^3 -3ab*cuberoot(2b)]

Answer 5

it is a cube root sign your refering to for instance the cube root of 8 is 2 because 2 x 2 x 2 = 8 so its the same as saying 8^(1/3)=2 get it? so you end up with

4ab cube root (b) - ab cube root (54 b)