1. Eliz and pka... thank you both very much. (I'm getting it. I'm gone.) John

2. Sooooooo:

show "radicand of n" this way : sqrt(n)

3x^2 = 3 times x^2

(3x)^2 = 9 times x^2

Mais oui, Jean ?

3. pka,
I did well with your first 2 examples, but the third:
(-xy^2)^4*(x^3y^2)^3 = (x^4y^8)(x^9y^6) = x^13y^14

is a puzzle (to me). The first parenthetical term: (-xy^2)^4

Isn't there an invisible "1" between the minus sign and the "x"? Raising "-1x" to the 4th power looks like (-1x)(-1x)(-1x)(-1x). Does this not require the "Same Sign Rule"... to keep the sign and add the numbers? Result would be (-x^4y^8)

Did you intentionally throw me a curve, or am I still thick?
John
PS A belated thank you, Denis.

4. What is (-1)<sup>4</sup>?

Eliz.

5. Eliz,
Thank you. 1 to the 4th power would be 1. The term is (-1x)^4. What happens to the minus sign?
John

6. Originally Posted by John Whitaker
The term is (-1x)^4. What happens to the minus sign?

Mr. Whitaker, you must learn the basic idea.

$\left( {ab} \right)^n = a^n b^n$ this is true period!
$\left( { - x} \right)^4 = \left( { - 1x} \right)^4 = \left( { - 1} \right)^4 \left( x \right)^4 = x^4$

For any even counting number n , $\left( { - x} \right)^n = x^n$.
Why? Because n is even, n=2j for some j, so
$\left( { - x} \right)^n = \left( { - x} \right)^{2j} = \left[ {\left( { - x} \right)^2 } \right]^j = \left( {x^2 } \right)^j = x^{2j} = x^n$

Now What happens to the minus sign?

7. Originally Posted by stapel
What is (-1)<sup>4</sup>?
Originally Posted by John Whitaker
1 to the 4th power would be 1
Yes, but that doesn't answer my question.

You are correct that (1)<sup>4</sup> = 1. But what is (-1)<sup>4</sup>?

Eliz.

8. Eliz,
(-1)^4... That would be "-1"
If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
John

9. Originally Posted by John Whitaker
Eliz,
(-1)^4... That would be "-1"
If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
John
I give up!
The dragon of confusion has slain George the reasonable!

10. Originally Posted by pka
Originally Posted by John Whitaker
Eliz,
(-1)^4... That would be "-1"
If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
John
I give up!
The dragon of confusion has slain George the reasonable!
You're not alone. I have no either what John is doing or trying to convey to us either.

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