Question

Help with algebra problem! Will medal and fan.
12x−2y−3+3(x+y)

Answer 1

\[12x^{-2}y ^{-3}+3(x+y) when x = 2 and y = -3 so, 12(2)^{-2}(-3)^{-3}+3(2+-3)\]

Answer 2

so the problem is to "evaluate"
\[ 12(2)^{-2}(-3)^{-3}+3(2+-3) \]

First, you need to know "order of operations"
second, you should know this rule for negative exponents:
\[ a^{-b}= \frac{1}{a^b} \]
(flip and change the sign of the exponent )

can you simplify this part: 3(2+ -3) ? what is that ?

Answer 3

Go to Mathway.com. They are really helpful.

Answer 4

@phi, would the final answer be 6-9... -3?

Answer 5

or would it be \[-3\div12(4)(9) = -3\div432\]

Answer 6

just the 3(2-3) part is 6 -9 = -3
(or you could do 2-3 first = -1 and 3*-1= -3 )

that means you have , so far,
\[ 12(2)^{-2}(-3)^{-3} - 3\]

now lets do just
\[ 2^{-2} \]
can you re-write that using the flip and minus the exponent rule?

Answer 7

\[12(-3)^-3-34\[12(-3^{3}) -3\div4\]

Answer 8

Is this right? 12(-3)^-3 -3 /4

Answer 9

\[ 2^{-2}= \frac{1}{2^2}= \frac{1}{2\cdot 2}= \frac{1}{4} \]

Answer 10

ok with just that step?

Answer 11

Yes. Makes sense.

Answer 12

so far, we have
\[ 12(2)^{-2}(-3)^{-3}+3(2+-3) \\
12(2)^{-2}(-3)^{-3} - 3 \\
12\cdot\frac{1}{4} \cdot (-3)^{-3} - 3 \]

we replaced the 2^-2 with 1 /4

Answer 13

now can you do
\[ (-3)^{-3} \]
using the flip and negate the exponent rule?

Answer 14

Quick question - on my worksheet the last part is written (x+y)3 or (2+-3)3 once the variables are changed - does that still result in the same answer?

Answer 15

is that (x+y)^3 or (x+y)*3 ?

Answer 16

So that would be 1/9

Answer 17

On my worksheet it is just a regular three. So unless it is a typo it is just (x+y)3

Answer 18

if it's multiply for (x+y)*3 then we are ok. But usually if we multiply we put the numbers in front of the letters... but for the moment let's ignore that.

back to (-3)^ -3
that is
\[ \frac{1}{(-3)^3} = \frac{1}{-3 \cdot -3 \cdot -3} \]

Answer 19

1/-27?

Answer 20

so 12(1/4)(1/-27)-3

Answer 21

yes. so far we have
\[ 12\cdot\frac{1}{4} \cdot\frac{1}{-27} - 3 \\

\]
notice we can simplify 12/4 to 3 to get
\[ 3 \cdot\frac{1}{-27} - 3 \]

Answer 22

or
\[ -\frac{3}{27} - 3 \]

Answer 23

what is -3/27 ?

it is -1/9

Answer 24

Yes so would the final answer be -1/9 - 3

Answer 25

which is , as a mixed number
\[ \frac{-1}{9}-\frac{27}{9} = - \frac{28}{9} \]

Answer 26

you might also write it as
\[ - 3 \frac{1}{9} \]
negative 3 and one-nineths

Answer 27

or
-3.111....

Answer 28

Thank you :)

Answer 29

ok, I hope the steps made sense.

Answer 30

They did!