Expert: Josh - 1/3/2006

Question
Hi, my math Q is 1 over 3(e^-3)^4 i am not good in math and dont know what to do we the "e".

Answer
The "e" is a "constant", with an approximate value of 2.7172.

To simplify this expression, you need to be aware of the "exponent laws". Let me review these.

Suppose a,b,c represent some arbitrary numbers.

Rule 1.When we raise a number "a" to an exponent "b" and raise the whole thing to another exponent "c", we have
(a^b)^c = a^(b*c)

e.g., if a=2, b=3, c=4, we have (a^b)^c=(2^3)^4
claim: From above, we should have (2^3)^4 = 2^12
To verify this, observe that (2^3)=8. Therefore, (2^3)^4=8^4=8*8*8*8=4096.

Rule 2.When we raise a number "a" to an exponent "b" and multiply this by "a" raised to another exponent "c", we have
(a^b)*(a^c) = a^(b+c) ...the exponents ADD in this case.

e.g., if a=2, b=3, c=4, we have (a^b)*(a^c)=(2^3)*(2^4)=8*16=128
check that this is equivalent to 2^(3+4)= 2^7.

Now, the question involving "e" is no different. Remember that "e" is just a constant. Treat it like any number, which we called "a" in the above.


Consider the part [e^(-3)]^4. This has the same form as [a^b]^c. What do we do? Ans: multiply the exponents as we've done before (quoting rule 1)

[e^(-3)]^4= e^(-3*4)=e^(-12)

Other parts are trivial. 3*((e^-3)^4) is obviously 3 e^(-12). Assuming you have typed correctly and I interpreted correctly. Taking the reciprocal, you can write the answer as (1/3) e^(12). How you give the answer depends on what the question asks for really.

Just be aware that a^(-1) = 1/a.