Question

Algebra help please. simplify (2^5a^9b^5)(2a_4b^3)/2^3a^6

Answer 1

\[\frac{ 2^5a^9b^5 \times 2a^4b^3}{ 2^3a^6 }\]

Answer 2

Yes

Answer 3

Well first of all, we can deal with the top first. We can combine those 2 terms since the base is the same. When multiplying with same base, just add exponents

Answer 4

\[x^{a}\times x^{b} = x^{a+b}\]

Answer 5

\[(2^5a^9b^5)(2a^-4b^3)/2^3a^6\]

Answer 6

What are you suggesting?

Answer 7

is my equation above wrong?

Answer 8

is that a subtraction or...

Answer 9

no...the numerator\[2a^-4 \not 2a^4\]

Answer 10

\[is this correct? 2^5a^9b^5\times 2a^-4b^3 = 2^3a^6\]

Answer 11

wait was my equation wrong?

Answer 12

i don't get your 2a-4b^3 part

Answer 13

The question is simplify \[(2^5a^9b^5)(2a^-4b^3)/2^3a^6\]

Answer 14

\[\frac{ 2^5a^9b^5 \times 2a^{-4}b^3 }{ 2^3a^6 }\] Is this it?

Answer 15

Yes

Answer 16

and you got \[2^3a^6?\]

Answer 17

No, not sure how to solve the problem

Answer 18

do you get the rule i stated above?

Answer 19

\[x^{a}\times x^{b} = x^{a+b}\]

Answer 20

Which is a and b?

Answer 21

example: (x^2)(x^3) = x^5
(xx)(xxx) = (xxxxx)

Answer 22

ok

Answer 23

that is just a general formula. let's start with the numerator. with the base 2

Answer 24

in bracket one we have 2^5 and bracket 2^1
(2^5)*(2^1) = ?

Answer 25

\[2^5a^9b^5\times2a^-4b^3\]

Answer 26

yes? we are doing the base 2 first. essentially the top is all multiplication \[2^{5}2a^9a^{-4}b^5b^3\] is the same thing

Answer 27

ok

Answer 28

so what do you get for combining the base 2 values ?

Answer 29

Or if you can do the whole numerator, that'd be great. I think it's pretty stright forward with the general rule and example I showed you

Answer 30

\[2a^9+-4b^5+3\]

Answer 31

what are you doing. can you explain?

Answer 32

\[2a^5b^8\]

Answer 33

CORRECT

Answer 34

\[2a^5b^8/2^3a^6\]

Answer 35

As for the denominator, it's subtraction of exponents

Answer 36

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

Answer 37

any exponents in the denominator brought to the numerator becomes negative

Answer 38

yes

Answer 39

\[a^5-a^6= -1\]

Answer 40

\[\frac{ x^a }{ x^b } = x^ax^{-b} = x^{a-b}\]

Answer 41

just the exponents. what happen to your 2?

Answer 42

\[a^{5-6} = a^{-1}\]

Answer 43

don't forget your b

Answer 44

\[2^2a^-1b^2\]

Answer 45

are you sure about your b term?

Answer 46

yes

Answer 47

sorry

Answer 48

why is it to the power 2

Answer 49

b^8

Answer 50

also, i just noticed that your 2 has wrong power from your previous numerator solution

Answer 51

you got 2a^5b^8 before. why is your 2 only to power 1?

Answer 52

no..2^2a^-1b^8

Answer 53

no i mean for the numerator only part

Answer 54

yes

Answer 55

\[2^{5} \times 2^1 = ?\]

Answer 56

\[2^5+2^3\]

Answer 57

no just the exponents

Answer 58

how am confused now

Answer 59

okay. your a and b are correct . it is the final answer. the a and b part

Answer 60

but your 2 is part is incorrect.

Answer 61

\[2^5a^9b^5 \times 2a^{-4}b^3\]

Answer 62

remember the two b's in the numerator is b^5 and b^3

Answer 63

that part is correct

Answer 64

what about the 2 coefficient

Answer 65

\[2^5 \times 2^1 = ?\]
\[a^9 \times a^{-4} = a^5\]
\[b^5 \times b^3 = b^8\]

Answer 66

we're going back to just the numerator multiplication only

Answer 67

no denominator yet. you solved the a and b correctly. we just need the 2 coefficient.

Answer 68

ok

Answer 69

You get it?

Answer 70

\[2^5a^9+-4b^5+3= 2^5a^5b^8\]

Answer 71

isn't it
\[2^5a^9b^5 \times 2a^{-4}b^3\]

Answer 72

ooh oh..you did subtraction with a?

Answer 73

isn't that the equation?

Answer 74

yes, the original equation

Answer 75

exactly. so how did you get your 2 to the power of 5? for the numerator only?

Answer 76

when 2 is alone, it is 2^1.
2^0 =1, 2^1=2, 2^2=4

Answer 77

2 is't alone, it is 2^5

Answer 78

you solved for a and b for the numerator and got \[a^5b^8\]

Answer 79

what about the second part isn't it \[2a^{-4}b^3?\]

Answer 80

yes, the second part is alone but the first isn't

Answer 81

yes so it is
\[2^5 \times 2^1= 2^?\]

Answer 82

2^6

Answer 83

imagine 2=c
\[c^5 \times c^1 =?\]

Answer 84

YAY! now do the denominator part to it as well! What do you get as your final answer?

Answer 85

\[2^3a^-1b^8\]

Answer 86

YES! That's the final answer.

Answer 87

\[2^3a^{-1}b^3\]

Once you get the hang of it. It isn't too bad right.

Answer 88

yes, and thanks for your patience

Answer 89

no worries. you can also expand the 2 \[8a^{-1}b^8\]

Answer 90

2x2x2 = 8
if your teacher prefers that way

Answer 91

ok