Question

cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5

Answer 1

Help Please!

Answer 2

@Haseeb96

Answer 3

@ilikemath50

Answer 4

Did not learn cube roots yet, Can't help you there, sorry

Answer 5

Dang

Answer 6

do you know anyone

Answer 7

I'll try to send someone else in, @precal @thomaster @iambatman

Answer 8

Thank you!

Answer 9

No problem! :)

Answer 10

Im new to this like I just started

Answer 11

@superhelp101

Answer 12

Yeah, when I just started all I did was ask questions, but im pretty good at math so I was like hey! why not help people with their questions? I have gotten quite a few medals and fans now.. I could do better though, lol

Answer 13

give me a moment to try to post the equation

Answer 14

Ok thanks :)

Answer 15

\[\frac{ \sqrt[3]{5}\sqrt{5} }{ \sqrt[3]{5^5} }\] is this your problem?

Answer 16

Yes

Answer 17

ok lets rewrite it using fractions

Answer 18

Ok

Answer 19

here are my answer choices

Answer 20

\[\frac{ 5^{1/3}5^{1/2} }{ 5^{5/3} }\]

Answer 21

don't need your choices

Answer 22

ok

Answer 23

ok what is x times x?

Answer 24

1

Answer 25

no x times x is x^2
(x to the second power)

Answer 26

Ohh

Answer 27

I understand that

Answer 28

why is this true? because we added the powers
so \[x^1(x^2)=x^3\]

Answer 29

ok we do need the same base for this to be true, btw this is one of your laws of exponents

Answer 30

so do the top of the fraction for me

Answer 31

ok you have to add the exponents

Answer 32

5 5/6

Answer 33

because i did 1/3 = 2/6 then 1/2 =3/6 right? @precal

Answer 34

yes it is 5 and 5/6

Answer 35

Yay ok now the next part

Answer 36

now this leads us to another law of exponent
\[\frac{ x^3 }{ x }\] is what?

Answer 37

\[\frac{ x^3 }{ x }=\frac{ xxx }{ x }=xx=x^2\]

Answer 38

do you see the pattern for this law of exponent?

Answer 39

ya

Answer 40

I see

Answer 41

so its 5 5/6 over 5 5/3

Answer 42

\[\frac{ a^b }{ a^c }=a ^{b-c}\]

Answer 43

Hold on i gtg fix my blinds be back

Answer 44

ok

Answer 45

let me know when to continue

Answer 46

k im back @precal I had new windows put in and They took my blinds down

Answer 47

no problem, I fixed mine the other days.....I would rather solve math problems than real world house problems.....

Answer 48

ok so the bases are the same and we are going to subtract the exponents. Always do top exponent minus bottom exponent

Answer 49

Ok

Answer 50

so its 5 5/6 minus 5 5/3

Answer 51

\[\frac{ 5^{5/6} }{ 5^{5/3} }\]

Answer 52

would I make it 10/6

Answer 53

\[5^{\frac{ 5 }{ 6}-\frac{ 5 }{ 3 }}\]

Answer 54

should be -5/6

Answer 55

THANK YOU

Answer 56

\[5^{-5/6}\]

Answer 57

How can I like favorite you

Answer 58

Im new

Answer 59

well we are not done, leads us to another law of exponent,

Answer 60

O ok

Answer 61

mark response look for the blue rectangle that states "best response" this gives us medals and you can "fan me" if you want, I think you have to pick something on my name.....

Answer 62

last step

Answer 63

\[x ^{-2}=\frac{ 1 }{ x^2 }\]

Answer 64

so we have 5 -5/6

Answer 65

negative powers move things from numerator to denominator
so x^-2 is a numerator and to get rid of the negative sign, we make it a denominator

Answer 66

\[\frac{ x^3y ^{-2} }{ z ^{-4} }\]

Answer 67

were did you get that?

Answer 68

ok see how y has a negative power and z has a negative power
I am making up an example to help you understand the last step

Answer 69

Yes o ok

Answer 70

\[\frac{ x^3y ^{-2} }{ z ^{-4} }=\frac{ x^3z^4 }{ y^2 }\]

Answer 71

see how y went to the bottom and z went to the top

Answer 72

ok yes

Answer 73

computer is acting weird, I need to get a new mouse

Answer 74

Ok lol

Answer 75

So is 5 -5/6 the answer?

Answer 76

Or is there another part

Answer 77

sorry, my computer is acting weird. I had to switch out three mouses

Answer 78

\[\frac{ 1 }{ 5^{5/6} }\]

Answer 79

this is your final answer

Answer 80

Its doesnt show

Answer 81

sometimes the system gets rid when there are a lot of people on the site

Answer 82

get weird I meant

Answer 83

can you see it now

Answer 84

O wait I just rembered that the properties of exponents shows that if you have a 1 over the answer that it can be made into a negative answer!!!! so 5 -5/6 is right!!

Answer 85

\(\Large \bf {
a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad

\sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}
\\\quad \\

a^{-\frac{{\color{blue} n}}{{\color{red} m}}} =
\cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}} \implies \cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}
\\ \quad \\ \quad \\

\frac{ \sqrt[3]{5}\sqrt[2]{5} }{ \sqrt[3]{5^5} }\implies \cfrac{5^{\frac{1}{3}}\cdot 5^{\frac{1}{2}}}{5^{\frac{5}{3}}}\implies \cfrac{5^{\frac{1}{3}}\cdot 5^{\frac{1}{2}}}{1}\cdot \cfrac{1}{5^{\frac{5}{3}}}
\\ \quad \\
5^{\frac{1}{3}}\cdot 5^{\frac{1}{2}}\cdot 5^{-\frac{5}{3}}\implies 5^{\frac{1}{3}+\frac{1}{2}-\frac{5}{3}=\frac{4+6-20}{12}=\frac{-\cancel{ 10 }}{\cancel{ 12 }}=\frac{-5}{6}}
\\ \quad \\
5^{\frac{-5}{6}}\implies \cfrac{1}{5^{\frac{5}{6}}}\implies \cfrac{1}{\sqrt[6]{5^5}}
}\)

Answer 86

THANK YOU GUYS SO MUCH ILL TELL YOU IF I GET IT RIGHT!!!

Answer 87

yes but it is best to get rid of negative exponents

Answer 88

anytime

Answer 89

I actually have a couple more ill post them

Answer 90

sure, close this problem out and open a new thread please