solving exponential equations, simplifying expressions

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Simplify. Express each answer with a positive exponent
1) (x/3) -1

. . .1/ x/3

2) ( -2x^-3 y)( -12x^-4 y^-2) / 6xy^-3

. . .24x^12 y^-2 / 6xy^-3

. . .18^-9x y^-1

. . .18^-9x / y^-1

Can someone please check these?

3) Solve (-8) ^ 1-2x = (-32) ^1-x

How do you do this?

4) Expand and simplify 3y [1- y(y-3) ] - [2 - y(y-4)]

3y [1- y(y-3) ] - [2 - y(y-4)]

. . .=3y (1- y<sup>2</sup> -3y) - (2 - y<sup>2</sup> -4y)

. . .=3y - 3y<sup>3</sup> - 9y<sup>2</sup> -2 +y<sup>2</sup> +4y

. . .=6y -3y<sup>3</sup> -8y<sup>2</sup> -2

5) Expand and simplify (2r + 3t)(r - t ) - 4 ( r - 2t )<sup>2</sup> + 5 ( r<sup>2</sup> - t<sup>2</sup> )

(2r + 3t)(r - t ) - 4 ( r - 2t )<sup>2</sup> + 5 ( r<sup>2</sup> - t<sup>2</sup> )

(2r + 3t)(r - t ) - 4 ( r - 2t )<sup>2</sup> + 5r<sup>2</sup> - 5t<sup>2</sup> )

(2r + 3t)(r - t ) - 4 ( r - 2tr + 4t^2 ) + 5r<sup>2</sup> - 5t<sup>2</sup>

(2r + 3t)(r - t ) - 4r<sup>2</sup> + 8tr - 16t<sup>2</sup> + 5r<sup>2</sup> - 5t<sup>2</sup>

2r<sup>2</sup> - 2rt +3rt -3t<sup>2</sup> -4r<sup>2</sup> +8rt - 16t<sup>2</sup> + 5r<sup>2</sup> - 5t<sup>2</sup>

3r<sup>2</sup> + 9rt + 24t<sup>2</sup>

Can some one tell me where I went wrong?

Thanks,
Aka
 
Re: silving equations

Aka said:
Simplify. Express each answer with a positive exponent
1) (x/3) -1
1/ x/3
Click to expand...
That's funny. While correct, I think it other than what was intended. :D

(x/3)<sup>-1</sup> = (3/x)<sup>+1</sup> = 3/x

If someone marks your answer "incorrect", I would like to have a chat with this grader. Also, I would like to have the chat with you that I already had, above.
 
1) This looks like "x-over-three, subtract one". Is that what you meant? And what do you mean by your answer? It looks like "one over x over three", which I don't understand.

2) Do you mean the following by the original expression?

. . . . .[(-2x<sup>-3</sup>y)(-12x<sup>-4</sup>y<sup>-2</sup>)] / [6xy<sup>-3</sup>]

3) You appear to have posted this:

. . . . .(-8)<sup>1</sup> - 2x = (-32)<sup>1</sup> - x

Is that what you meant? Or did you mean something else, such as the following?

. . . . .(-8)<sup>1 - 2x</sup> = (-32)<sup>1 - x</sup>

4) Check your signs. For instance, -y(-3) does not equal -3y; instead, -y(-3) = +3y.

5) Check your expansions. For instance:

. . . . .(r - 2t)<sup>2</sup>

. . . . . . .= (r - 2t)(r - 2t)

. . . . . . .= r<sup>2</sup> - 2rt - 2rt + 4t<sup>2</sup>

. . . . . . .= r<sup>2</sup> - 4rt + 4t<sup>2</sup>

Thank you, by the way, for showing your steps! :D

Eliz.
 
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