Question

explain how all of the following expressions have the same answer.

Answer 1

well, they're all "blank", thus they all have the same answer, which is "blank", easy

Answer 2

haha yea sorry it took a while to put a picture up

Answer 3

what would you get when simplifying \(\bf \large \sqrt[3]{x^3}\quad ?\)

Answer 4

idk um x^1?

Answer 5

ok... so now let's see the following one \(\bf \large {\sqrt[3]{x^3}\implies x\\ \quad \\
x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\implies x^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1}\implies x^1=x}\)

what about the next one \(\bf \cfrac{1}{x^{-1}}\quad ?\)

Answer 6

i really dont know i dont get it

Answer 7

keep in mind that \(\bf a^{-n} = \cfrac{1}{a^n}\)

Answer 8

x^-1?

Answer 9

you could use this thinking: all have the same answer... the first two simplify to x
so you should expect the remaining two will also simplify to x
you now need the reason for this happens.

Answer 10

*why this happens

Answer 11

ok thank you

Answer 12

for the third on your list, see http://www.freemathhelp.com/negative-exponents.html

It is just a "rule"

Answer 13

For the last one, see
http://www.dummies.com/how-to/content/how-to-convert-square-roots-to-exponents0.html

Answer 14

thnk you so much that really helps

Answer 15

\(\bf \cfrac{1}{x^{-1}}\implies x^{-(-1)}\implies x^1=x\)

Answer 16

\(\bf \large \sqrt[11]{x^5\cdot x^4\cdot x^2}\implies \sqrt[11]{x^{5+4+2}}\) anyhow

Answer 17

yea and then that equals to \[\sqrt[11]{x ^{11}}\] then i get x

Answer 18

yeap

Answer 19

thank you

Answer 20

yw