1. Exponent Laws

I want to know about exponent laws properly. Someone can help me !

Thanking you

2. Re: Exponent Laws

The "exponent laws" are:

$(a^x)(a^y)= a^{x+ y}$
and

$(a^x)^y= a^{xy}$.

To see why those are true, notice that $a^3= (a)(a)(a)$ and $a^2= (a)(a)$. Multiplying [tex]a^3a^2= [(a)(a)(a)][(a)(a)]= (a)(a)(a)(a)(a)= a^5= a^{2+ 3}[tex] and
$(a^2)^3= (a^2)(a^2)(a^2)= ((a)(a))((a)(a))((a)(a))= a^6= a^{2(3)}$

3. Re: Exponent Laws

Just two additions. They can be derived from the list HallsofIvy gave you, but I'm listing them for reference.
1) $a^{-n} = \frac{1}{a^n}$

2) $a^0 = 1$, so long as $a \neq 0$.

-Dan

4. Re: Exponent Laws

And I would add this one as well, which can also be derived from HallsofIvy's post:

$a^{1/n} = \sqrt[n] a$

5. Re: Exponent Laws

another:
if a^p = x then p = log(x) / log(a)

6. Re: Exponent Laws

Originally Posted by DenisB
another:
if a^p = x then p = log(x) / log(a)
Technically that's a logarithm law.

-Dan

8. Re: Exponent Laws

Originally Posted by topsquark
2) $a^0 = 1$, so long as $a \neq 0$.
You sure?!

9. Re: Exponent Laws

Originally Posted by DenisB
yep ...

11. Re: Exponent Laws

Originally Posted by topsquark
Technically that's a logarithm law.

-Dan
"Logarithm" is literally another word for "Exponent". Every logarithm law is also an exponential law hahaha.

12. Re: Exponent Laws

Originally Posted by DenisB
last paragraph by the "mathematician" from the above link ...

There are some further reasons why using 0^0 = 1 is preferable, but they boil down to that choice being more useful than the alternative choices, leading to simpler theorems, or feeling more “natural” to mathematicians. The choice is not “right”, it is merely nice.