Question

One of your friends sends you an email asking you to explain how all of the following expressions have the same answer.
the cube root of x cubed

:x to the one–third power • :x to the one–third power • x to the one–third power

1 over x to the –1 power

the eleventh root of the quantity of x to the fifth times x to the fourth times x squared
Compose an email back assisting your friend and highlight the names of the properties of exponents when you use them.

Answer 1

@habibmatatta
help!

Answer 2

@mattdogg help

Answer 3

ok so first off you need to write out all the equations.

Answer 4

ok

Answer 5

the cube root of x cubed

:x to the one–third power • :x to the one–third power • x to the one–third power

1 over x to the –1 power

the eleventh root of the quantity of x to the fifth times x to the fourth times x squared

Answer 6

i meant the actual math like with the numbers and signs.

Answer 7

so the first one would be:
(x^3)^(1/3)

x^(1/3) x^(1/3) x^(1/3)

1/(1/x)

(x^5 x^4 x^2)^(1/11)

Answer 8

what i typed are the same thing but without the signs because i cant type those

Answer 9

1st the cube root and the cube exponent cancel out so it simplifies to x

2nd its the same thing as the first one except the cube root is on the inside and the exponent is on the outside but we still get the same answer which is x.

3rd 1/x^-1=1/(1/x)=x

4th x^5(x^4)(x^2)=x^11 and like the first and second one the 11th root cancels the 11th power out giving you x

Answer 10

did that make sense?

Answer 11

@dee_faulkner?