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

Answer 1

Can anyone help please ? i really suck at this

Answer 2

rules of exponents

labeling each section above as a, b, c d
a) cubed root = raised to the power 1/3
(x^3)(1/3) = x^1 = x


b) raise the power to a power multiply
x^(1/3)^3= x^(1/3)(3) = x(1) = x

c) 1/(x^-1 )
1/ (1/x )
to divide by fraction invert and multiply
(1)(x/1) = x

d) (x^5)(x^4)(x^2)^(1/11)
multiply with the same base add the exponents
base = x
5 + 4 + 2 = x^11^1/11 = x ^1 = x

Answer 3

thank you so much ! well explained. your awesome.

Answer 4

your welcome