Question

Simplify the given expression to radical form, justify each step by identifying the properties of rational exponents used. All work must be shown.

Answer 1

@satellite73

Answer 2

book keeping
your job is to subtract \(\frac{2}{3}-\frac{4}{9}\)

Answer 3

that will be your exponent
k?

Answer 4

I doubt it, it says show all work. Thats too little of an answer

Answer 5

lol you have to subtract!

Answer 6

I dont know how to subtract fractions .. ?

Answer 7

what is
\[\frac{2}{3}-\frac{4}{9}\]? that is all the work

Answer 8

2 -4 = -2

3-9= -6

Answer 9

oh well that is a bit of a problem
rewrite the first one by multiplying top and bottom by 3 to get
\[\frac{2}{3}\times \frac{3}{3}=\frac{6}{9}\] then you have
\[\frac{6}{9}-\frac{4}{9}\] subtract in the numerator (top) leave the denominator alone

Answer 10

you get
\[\frac{6}{9}-\frac{4}{9}=\frac{2}{9}\] making your answer
\[\large x^{\frac{2}{9}}\]

Answer 11

I got that !! :D

Answer 12

does this ring a bell?

Answer 13

Do I need to apply more step or do I leave it at 2 over 9 ?

Answer 14

you do not add fractions or subtract by adding or subtracting top and bottom
yes, leave it like that

Answer 15

you cannot reduce \(\frac{2}{9}\)

Answer 16

My main question is what work do I show ? what does it mean by " Justify each step" ?

Answer 17

ooh it says "radical form"
ok you have to write
\[\large x^{\frac{2}{9}}=\sqrt[9]{x^2}\]

Answer 18

i don't know exactly what "justify each step" means
it is always the case that
\[\frac{x^n}{x^m}=x^{n-m}\] and so
\[\large \frac{x^{\frac{2}{3}}}{x^{\frac{4}{9}}}=x^{\frac{2}{3}-\frac{4}{9}}\]

Answer 19

then when you subtract you get
\[\large x^{\frac{2}{9}}\] and writing with radical notation gives
\[\large x^{\frac{2}{9}}=\sqrt[9]{x^2}\]

Answer 20

okay i'll write that and see if anything ill ask my teacher cause im really not sure either. Im asking SO many questions because all teachers are going to be out for the week so i cant get help from them till monday the 23rd i believe

Answer 21

there's also this one ( this one is the last one)

Answer 22

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 23

they are all \(x\)

Answer 24

\[\sqrt[3]{x^3}=x\] is obvious because it means the cubed root of the cube

Answer 25

\[x^{\frac{1}{3}}\times x^{\frac{1}{3}}\times x^{\frac{1}{3}}=x\] because when you multiply you add the exponents, and \(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1\) giving \(x^1=x\)

Answer 26

\[\frac{1}{x^{-1}}=x\] because the minus sign in the exponent means take the reciprocal, and the reciprocal of \(\frac{1}{x}\) is \(x\)

Answer 27

Gotcha ! thankyouuu :]

Answer 28

\[\sqrt[11]{x^5\times x^4\times x^2}=\sqrt[11]{x^{5+4+2}}=\sqrt[11]x^{11}\] and
\[\sqrt[11]{x^{11}}=x\] for the same reason that \(\sqrt[3]{x^3}=x\)

Answer 29

so which one do i write for that one ? all of that including that last one ?

Answer 30

there were several parts
i answered all of them
the last one was for the last part