Question

Rewrite without rational exponents, and simplify, if possible. 49^3/2

Answer 1

with a rational exponent, the numerator is the power and the denominator is the root

Answer 2

making this
\[\sqrt{49^3}\] take the square root first, cube second

Answer 3

so i guess it would be easier if you write \(\sqrt{49}^3\)

Answer 4

where did the 2 go? I'm sorry i suck at radical problems!

Answer 5

the two in the denominator means take the "square root"

Answer 6

notice that the problem says exactly
"Rewrite without rational exponents"
when you get rid of the rational exponent, the 2 in the denominator becomes the square root sign

Answer 7

so since 7 times 7 is 49 would i then do 49^3?

Answer 8

you could write
\[49^{\frac{3}{2}}=\sqrt[2]{49^3}\] but no one writes an "index" of two

Answer 9

or 7^3

Answer 10

ahhh ok

Answer 11

the second one

Answer 12

as you said, \(7\times 7=49\) which means \(\sqrt{49}=7\)

Answer 13

so 343 is the answer?

Answer 14

therefore
\[\sqrt{49}^3=7^3=343\] yes you are right

Answer 15

ahhh ok, that makes sense! thank you!

Answer 16

yw
you got more or is that it?

Answer 17

I have a lot more problems with radicals!!!! One of my other questions says Rewrite with positive exponents, and simplify if possible? would i do the same thing one of the problems is 27^-1/3

Answer 18

this one is a little different because of the minus sign in the exponent

Answer 19

\[\large 27^{\frac{1}{3}}=\sqrt[3]{27}\] see this time you write the index because of the cubed root
do you know what the cubed root of 27 is?

Answer 20

3

Answer 21

got it

Answer 22

now the minus sign in the exponent does not mean make it negative, it means take the reciprocal, in other words, flip it
do you know what the reciprocal of 3 is ( don't think too hard)

Answer 23

-3?

Answer 24

or 1/3

Answer 25

nah you fell for it
don't make it negative
take the reciprocal

Answer 26

second one

Answer 27

so
\[\large 27^{-\frac{1}{3}}=\frac{1}{\sqrt[3]{27}}=\frac{1}{3}\]is the right answer

Answer 28

still need help?

Answer 29

that one makes sense, can you help me with a different question?

Answer 30

yes of course

Answer 31

thanks, another questions says use the laws of exponents to simplify. Write the answers with positive exponents. 5^3/4 * 51/8

Answer 32

i take it this is
\[\large 5^{\frac{3}{4}}\times 5^{\frac{1}{8}}\] right?

Answer 33

your job here is only to add \(\frac{3}{4}+\frac{1}{8}\) to get the exponent

Answer 34

yes, and 7/8

Answer 35

you are right
since
\[\frac{3}{4}+\frac{1}{8}=\frac{6}{8}+\frac{1}{8}=\frac{7}{8}\] your answer is
\[\large 5^{\frac{7}{8}}\]

Answer 36

thats it? thats easy!

Answer 37

yeah adding exponents is pretty easy if you can add
some people get stuck at adding fractions
any more?

Answer 38

haha yah! if thats ok?

Answer 39

yeah sure

Answer 40

it says use rational exponents to simplify. write the answer in radical notation if appropriate.
\[(\sqrt[3]{ab})\]^15

Answer 41

sorry the ^15 is supposed to be right next to the equation

Answer 42

\[\large\left(\sqrt[3]{ab}\right)^{15}\] right?

Answer 43

yup

Answer 44

you are going to be amazed (maybe) at how easy this one is
how many times does 3 go in to 15?

Answer 45

5 times

Answer 46

ok so the answer is \(\left(ab\right)^5\)

Answer 47

wow that is easy! thanks

Answer 48

don't forget you can go backwards too
\[\sqrt[3]{x}=x^{\frac{1}{3}}\] so
\[\large \sqrt[3]{x}^{15}=x^{\frac{15}{3}}=x^5\]

Answer 49

yeah and at the beginning you said you sucked at radicals if i recall...

Answer 50

any more of these?

Answer 51

haha yah, i just get confused by the different questions i guess!

Answer 52

nd yah, but i have to go back and apply this to some other questions first, so im good for a little bit! thanks!!

Answer 53

yw
good luck, hope this helped