Question

(2a^3b^-2) (-4a^2b^4)
i dont understand..

Answer 1

step by step
what is \(2\times -4\) ?

Answer 2

−8a^5b^2

Answer 3

could you explain?

Answer 4

\(2\times -4=-8\)\[a^2\times a^3=a^{2+5}=a^5\]
\[b^4\times b^{-2}=b^{4-2}=b^2\]

Answer 5

i thought i had to get rid of negative powers first

Answer 6

nah, just add up the exponents for the like terms

Answer 7

soo 2*-4 then add the exponents n then 1b+b1 then add-2 and 4 ?

Answer 8

not sure what you mean by 1b+b1

Answer 9

dont the bs have an understood one

Answer 10

\[\large (2a^3b^{-2}) (-4a^2b^4)\] lets put the like terms next to each other
\[\large 2\times -4\times a^3\times a^2\times b^{-2}\times b^4\]

Answer 11

clear where the \(-8\) comes from right?

Answer 12

2a^3+-4a^2

Answer 13

oh i see the confusion
it is all multiplication, there is not addition here

Answer 14

simplifing

Answer 15

the coefficients (numbers) are not attached to the variables.
you multiply them together, they are numbers

Answer 16

it is a multiplication, not an addition
btw there is no such mathematical operation as "simplify"
that is the lazy math teachers way of writing "give me an answer i want"
you can add, subtract, multiply, divide
in this case you are supposed to multiply

Answer 17

but here when you multiply \(a^3\times a^3\) you get \(a^{2+3}=a^5\) i.e. you add the exponents

Answer 18

oops typo there, i meant \(a^2\times a^2=a^{2+3}=a^5\)

Answer 19

oops my bad i forgot :/

Answer 20

\[\overbrace{a\times a}^{a^2}\times \overbrace{a\times a\times a}^{a^3}=\overbrace{a\times a\times a\times a\times a}^{a^5}\]

Answer 21

i dont understand that

Answer 22

the meaning of \(a^2\) is \(a\times a\) right?

Answer 23

oh

Answer 24

similarly \(a^3\) means \(a\times a\times a\)

Answer 25

oh ok ya i did know that

Answer 26

that was my explanation of why \(a^2\times a^3=a^5\)

Answer 27

similarly \(b^{-2}\times b^4=b^{-2+4}=b^2\)

Answer 28

so for this problem you had to do three things:
\(2\times -4=-8\) and \(a^2\times a^3=a^5\) and also \(b^{-2}\times b^4=b^2\) giving a final answer of
\[-8a^5b^2\]

Answer 29

ohh ok gotcha thankyou