Question

Simplify cube root of 7 over fifth root of 7.

7 to the power of 1 over 5
7 to the power of 8 over 15
7 to the power of 5 over 3
7 to the power of 2 over 15
@iGreen. im so confused

Answer 1

Can you draw or write your problem out for me?

Answer 2

Alright, now change both the numerator and denominator into fractions.

Answer 3

do what

Answer 4

Remember, \(\large \sqrt[n]{x^m} =x^{m/n}\)

Answer 5

im really confused about this kinda stuff

Answer 6

jus work with me here, you will learn.

Answer 7

ok

Answer 8

Take the numerator, the power ontop of the 7 is 1. The power of the square root is 3.

When writing is as a fraction, the power of the root becomes the denominator of the fraction.

Answer 9

Now can you write the numerator as a fraction for me?

Answer 10

uhm so now 7 is 1?

Answer 11

7 is not one, just think of the format here: \[\huge \sqrt[\color{red}{n}]{x^\color{blue}{m}} =x^{\color{blue}{m}/\color{red}{n}} \implies \sqrt[\color{red}{3}]{7^\color{blue}{1}}=~?\]

Answer 12

Think of your 7 like the x.

Answer 13

so when i did the math i got the total answer of 5.77377402739is that right

Answer 14

There is an easier way to go about finding the answer, just follow my method :P

Answer 15

but im pretty sure that is correct.

Answer 16

Yuor answer does not fit any of your answer choices.

Answer 17

oh okay

Answer 18

So what is the numerator as a fraction? cmon! you got this.

Answer 19

If we change both the numerator and denominator into fractions when we can subtract them and it will give us a much more simplified answer.

Answer 20

Ok, I will help you with the numerator, but you must write the denominator in the same way.

Answer 21

okay

Answer 22

\[\huge \sqrt[\color{red}{n}]{x^\color{blue}{m}} =x^{\color{blue}{m}/\color{red}{n}} \implies \sqrt[\color{red}{3}]{7^\color{blue}{1}}=7^{\color{blue}{1}/\color{red}{3}}\] Tell me if you understand what I did, because you will write the denominatr in the same way, just like this.

Answer 23

so the next one will be 7^1/5

Answer 24

Yes!! :)

Answer 25

So now we have \[\huge \frac{7^{1/3}}{7^{1/5}} = 7^{(1/3) - (1/5)}\]

Answer 26

Do you know how to subtract fractions?

Answer 27

\[\frac{1}{3}-\frac{1}{5}\]

Answer 28

find the least common denomiantor then add what you did to the bottom to the top then subtract

Answer 29

Ok, and so what will you get? :)

Answer 30

6/15-3/15

Answer 31

not quite 6/15

Answer 32

5/15

Answer 33

Yes :)

Answer 34

So (5-3)/15 =?

Answer 35

2/15

Answer 36

Good, :)

Answer 37

\[\huge \frac{7^{1/3}}{7^{1/5}} = 7^{(1/3) - (1/5)} = 7^{2/15}\]

Answer 38

D

Answer 39

And which answer choice would that be?

Answer 40

Great!