# exponents

### exponents

2^2 + 2^2 = 8 or is it
2^2 + 2^2 =4^2 (which would be 16)
DeValera

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### Re: exponents

$$a^n \times a^m = a^{n+m}$$

$$a^n + a^m =$$ there are no such a formula

But if we have $$m > n$$ we can write
$$a^n + a^m = a^n(1 + a^{m-n})$$

$$a + a =2a$$ where $$a = 2^2$$
So
$$2^2+2^2 = 2\cdot 2^2=2\cdot 4$$
Guest

### Re: exponents

Or for this particular case $$2^2+ 2^2= 4+ 4= 8$$.

If it were "*" rather than "+" then it would be $$2^2*2^2= 4*4= 16$$.

Be careful what your operation is!
Guest

### Re: exponents

You appear to be asking if $a^2+ b^2= (a+ b)^2$. The answer to that is a loud NO!

$(a+ b)^2= (a+ b)(a+ b)= a(a)+ a(b)+ b(a)+ b(b)= a^2+ 2ab+ b^2$, NOT $a^2+ b^2$.

HallsofIvy

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