1. ## Create expressions

Hi guys,

Create four expressions that, when simplified using the exponent laws, are equal to 4x^6
Each expression should use at least one different exponent law. State which law(s) must be used to simplify each expression.

Could somebody help me with that task and explain how to start creating expressions? Thanks.

2. ## Re: Create expressions

For example, $\displaystyle 4x^2\cdot x^4 = 4x^6$. You use the fact that $\displaystyle x^a\cdot x^b=x^{a+b}$.

3. ## Re: Create expressions

All the previous examples posted by you has demonstrated addition,subtraction,multiplication and division of exponents. Create example based on these facts and post your attempt.

Kalyan.

4. ## Re: Create expressions

Kalyan could you do me a favour and check my post "Trigonometry Word Wheel". I would really appreciate it to hear your opinion.

5. ## Re: Create expressions

So my expressions=

1. Product Law = (4x^2) (x^4) = 4x^6

2. Quotient Law = 4x^8
------
4x^2

= 4x^6

3. Power of a Power Law = (4x^3)^2 = 4x^6

4. Power of a Product Law = (4x^2) (x^4) = 4x^6

Is that right?

6. ## Re: Create expressions

1. and 4. are the same. The only missing expression is $\displaystyle \sqrt{16x^{12}} = 4x^6$. This in fact similar operation as 2. with the only exception that you are taking a fraction exponent.

Kalyan.

7. ## Re: Create expressions

What Law is it then? The missing expression?

8. ## Re: Create expressions

Originally Posted by ford2008
2. Quotient Law = 4x^8
------
4x^2

= 4x^6

3. Power of a Power Law = (4x^3)^2 = 4x^6
The coefficients (the numbers before x) in 2 and 3 are wrong.

9. ## Re: Create expressions

Thank you emakarov,

so it should be in 2 =

16x^8
------
4x^2

and in 3 =

(16x^3)^2

Is that right? Do you know witch missing expression law kalyanram is meaning with his answer?

10. ## Re: Create expressions

#3 should be $\displaystyle (2x^3)^2=4x^6$

11. ## Re: Create expressions

Originally Posted by ford2008
Do you know witch missing expression law kalyanram is meaning with his answer?
$\displaystyle \sqrt[a]{x^b}=x^{b/a}$.