Basic Middle School Math Help! Algebra Two, please open and help!?

Question

My sisters math problem, it says "evaluate the expression", and thats it, which means simplify were guessing.

1. 27 4/3
she started to evaluate it, and has
27 to the third power inside of the square root symbol,
with a three over top of the check part.
Please help! I'm gussing that the teacher wants you to simplify it using sqare roots, obviously.

Thanks!

Answer 1

is that "twenty seven and four thirds" ... if not please re-write (or spell it out in words)

1,
twenty seven and four thirds (27 & 4/3) is the same as
twenty seven and three thirds and one third (27 +1 + 1/3) = twenty eight and one third (IE 28 & 1/3). Principle is adding mixed numbers.

2, two hundred and seventy-four divided by (aka "over") three [IE (274)/3 ]is the same as ninety-one and one third (91 & 1/3). Principle is solving improper fractions

3, twenty seven raised to the power of four thirds is the same as saying the cubed root of 27 to the fourth power ... IE ³√(27) ⁴ which is the same as three to the fourth power, which is 81
... 27 ^ (4/3) = ³√(27) ⁴ = ³√(3*3*3) ⁴= 3⁴ = 3*3*3*3 = 81
... the principle on this one is anything to the power of (1/x) is the same as that same anything to the "x" root .. IE 2 ^1/4 is the same as the "fourth" root of 2

It sounds like your sister had:
³√27³ this means the cubed root or 27 cubed, which as you can imagine just means 27

Answer 2

From the start, the answer is 27 since the two cancel out. BTW, the ''check symbol" is called a shelf and the "square root symbol" is called a radical.
You can also write it like this. (27^3)^1/3. Using exponent rules, you multiply the two when coming into contact with an outside exponent. 3(1/3) is equal to one.

Also, you can set it up as an equation.
(27^3)^1/3(3)=x(^3)
(27^3)^1=x^3
27^3(1/3)=x^3(1/3)
27=x

I just noticed it is 27^4/3
27^4/3=27^(4 x 1/3)
27^(4 x 1/3)=27(^1/3)=3^4=81

Answer 3

Ok... You have 27^(4/3)

You can take the cube root of 27 first, which is 3, and then raise that to the fourth power which makes it 81.

Answer 4

27 (3/3=1*27=27. eh.. like that, since a 3 over the check means a cube, and the 27^3 means 27 cubed).

Answer 5

if you meant to write 27 ^(4/3) then it will be the cube root of 27,'3', raised to the fourth power...oh jinks...I can't work out THAT ! Is it 81^2 ???

Answer 6

27/3= 9/3= 3*3*3*3= 81

Answer 7

27 = 3^3

So (3^3) ^4/3 so that becomes 3^(4*3/3)= 3^4 = 81

Answer 8

27^(4/3)
do this first 27^1/3=3
then 3^4=81