1. ## Exponents

Ok hopefully last time I will bug you guys about exponents .

Simplify, leave without radicals and negative exponents.

(sqrt(m+2))(2+m)^3/2

and

(sqrt(e^(2x))

Any help is much appreciated~

2. Originally Posted by JonathanEyoon
Ok hopefully last time I will bug you guys about exponents .

Simplify, leave without radicals and negative exponents.

(sqrt(m+2))(2+m)^3/2

and

(sqrt(e^(2x))

Any help is much appreciated~
Try using these rules:
$\displaystyle \sqrt{x} = x^{1/2}$

and
$\displaystyle a^n \cdot a^m = a^{n + m}$

and
$\displaystyle (a^n)^m = a^{n \cdot m}$

-Dan

3. Originally Posted by JonathanEyoon

Simplify, leave without radicals and negative exponents.

A) (sqrt(m+2))(2+m)^3/2

and

B) (sqrt(e^(2x))
Hello,

to A):

$\displaystyle \sqrt{m+2} \cdot (2+m)^{\frac32} = (m+2)^{\frac12}\cdot (m+2)^{\frac32} = (m+2)^{\frac12 + \frac32} = (m+2)^2$

to B):
$\displaystyle \sqrt{e^{2x}} = \sqrt{\left(e^x \right)^2} = e^x$

4. Originally Posted by topsquark
Try using these rules:
$\displaystyle \sqrt{x} = x^{1/2}$

and
$\displaystyle a^n \cdot a^m = a^{n + m}$

and
$\displaystyle (a^n)^m = a^{n \cdot m}$

-Dan

Ok using the rules you gave me, I think I figured out the first one

(sqrt(m+2))(2+m)^3/2

is the same as

((m+2)^(1/2))((m+2)^(3/2)) = (m+2)^2. If this is correct, from here should I foil?

For the second one...

Can I have a little help starting off

5. Originally Posted by earboth
Hello,

to A):

$\displaystyle \sqrt{m+2} \cdot (2+m)^{\frac32} = (m+2)^{\frac12}\cdot (m+2)^{\frac32} = (m+2)^{\frac12 + \frac32} = (m+2)^2$

to B):
$\displaystyle \sqrt{e^{2x}} = \sqrt{\left(e^x \right)^2} = e^x$

Hi thanks for the answer!! But I still don't understand how you got the answer for part B . Could you walk me through it?

6. Originally Posted by JonathanEyoon
(sqrt(e^(2x))
$\displaystyle \sqrt{e^{2x}} = \left ( e^{2x} \right ) ^{1/2}$

Does this help?

-Dan

7. Originally Posted by JonathanEyoon
Ok using the rules you gave me, I think I figured out the first one

(sqrt(m+2))(2+m)^3/2

is the same as

((m+2)^(1/2))((m+2)^(3/2)) = (m+2)^2. If this is correct, from here should I foil?
Check with your teacher, but this form is probably fine.

-Dan

8. Originally Posted by topsquark
$\displaystyle \sqrt{e^{2x}} = \left ( e^{2x} \right ) ^{1/2}$

Does this help?

-Dan

Thanks!!! That helped quite a bit!

9. Hey final one!!.... I think haha

[35(2b+1)^(3) / 7(2b+1)^(-1)]^2

I factored out a 7 and did some other stuff leaving

[5(2b+1)^(4)]^2

From here I'm stuck

10. Originally Posted by JonathanEyoon
[35(2b+1)^(3) / 7(2b+1)^(-1)]^2

I factored out a 7 and did some other stuff leaving

[5(2b+1)^(4)]^2

From here I'm stuck
Hello,

your result is correct. Now use :

$\displaystyle (a \cdot b^n)^m = a^m \cdot b^{nm}$

For confirmation only: $\displaystyle 25 \cdot (2b+1)^8$

11. Originally Posted by earboth
Hello,

your result is correct. Now use :

$\displaystyle (a \cdot b^n)^m = a^m \cdot b^{nm}$

For confirmation only: $\displaystyle 25 \cdot (2b+1)^8$

From 25(2b+1)^8

Is that the simpliest form?

12. Originally Posted by JonathanEyoon
From 25(2b+1)^8

Is that the simpliest form?
Hello,

I don't know a way to simplify this term, so this result must be sufficient.

In short: Yes.