Question

Simplify 8^-4/3

Answer 1

Do you know how to express 8 in exponent form? i.e. looking like a^b?

Answer 2

that's another way of saying, do you know a number that will multiply itself multiple times to get 8?

Answer 3

no

Answer 4

ok. give me all the numbers you know that multiply each other to give 8

Answer 5

1,2,4

Answer 6

good, but please be more specific. what times what?

Answer 7

1*8 2*4

Answer 8

great. now would you agree with me that 2*4 = 2*2*2?

Answer 9

yes

Answer 10

2^3=8 oh thats what
you meant

Answer 11

yes. that's how to write 8 in exponent form

Answer 12

so back to the original question

Answer 13

ok

Answer 14

8^-4/3

Answer 15

Since we've written 8 in exponent form as 2^3, simply substitute it into the original equation

Answer 16

so its a fraction

Answer 17

no... exponents are different from fractions

Answer 18

the_lefay can i give the answer
or you will explain him all the way?

Answer 19

Carlosjaime, thanks but i will explain all the way. Understanding how it is worked is better than the answer :) The answer is good for today, but the explanation is good forever

Answer 20

alright back to the original question: 8^-4/3 = (2^3)^-4/3 = (2)^(3*-4/3) = 2^-4 = 1/(2^4) = 1/16

Answer 21

do you understand how i did that?

Answer 22

a little

Answer 23

lemme know what part you don't get

Answer 24

the = (2)^(3*-4/3)

Answer 25

= 2^-4 = 1/(2^4) = 1/16

Answer 26

that part

Answer 27

wow he left

Answer 28

Another way to think about it:

\[8^{-\frac{ 4 }{ 3 }} = \frac{ 1 }{ 8^{\frac{ 4 }{ 3 }} }\]

if you use the inverse rule, the negative sign on the exponent goes away.

for the exponents in fractions, it's always power over root

Answer 29

ok thank you i understand that way

Answer 30

ok do you get the power over root?

Answer 31

yea

Answer 32

whats that

Answer 33

sorry had to leave for a second

Answer 34

\[5^{\frac{ 2 }{ 3 }}\] is the same as \[\sqrt[3]{5^{2}}\]

Answer 35

ok yea i know what that is

Answer 36

So the 2 in the numerator becomes the power inside of the cubed root

Answer 37

yea i get it

Answer 38

Just to make sure, fill in the blanks for me.

Answer 39

\[8^{\frac{ 4 }{ 3}}= \sqrt[A]{8^{B}}\]

What is A? What is B?

Answer 40

a=3 b=4

Answer 41

Awesome! Great job Desi.

Answer 42

Good explanation @MissMai

Answer 43

thank you

Answer 44

Lemme get back to the original question and the pieces you didn't understand

Answer 45

you taught me so yea

Answer 46

8^-4/3 = (2^3)^-4/3 = (2)^(3*-4/3) = 2^-4 = 1/(2^4) = 1/16

Answer 47

8^-4/3 = (2^3)^-4/3 is where we convert 8 into exponent form 2^3

Answer 48

@MissMai ways easier sorry

Answer 49

oh lol i wasn't done. but it's not a competition. if you know how to solve it then good luck.

Answer 50

ok

Answer 51

lol...different minds think differently...however, efficiency is important...especially on timed tests!