How do I simplify this?

Question

Simplify:

X^(-3x-4)^3

Answer 1

This problem might be a little ambiguous

Consider a simple example to see better how exponents work.

2^2^3 = 2^6 ( the exponents multiply, 2x3=6)

= 2x2x2x2x2x2 = 64

which is the same as (2^2)^3 = 4^3 = 4x4x4 = 64

So, multiply the exponent 3 times -3x-4 to get

x^(-9x-12)

It could be rewritten as x^-(9x-12) or

1/(x^(9x-12))

About the only other possibility is

if the problem had more parentheses, explicit or implicit:

x^[(-3x-4)^3]

then the expression = x^(cube of -3x-4)

cube of a binomial has coefficients 1,3,3,1 with terms (-3x)^3, (-3x)^2(-4), (-3x)(-4)^2, (-4)^3

or

x^(-27x^3+36x^2-36x-64) which could be rewritten as a product of four terms

(x^-27x^3)(x^36x^2)(-x^36x)(-x^64)

this "simplification" is similar to 2^(2^3) = 2^8 = 256

But if you say the instructor said the answer is to just ignore the exponent 3, I have no idea how he could do that. x^(-3x-4)^3 does not equal x^(-3x-4). There must be some more to this problem. Some missing information or assumption.

Maybe he meant

x^(-3x-4)^3 = [x^(-3x-4)][x^(-3x-4)][x^(-3x-4)]

that's true