Question

What solves the p equation p to the -5th power = 1/243

Answer 1

p = 3

Explanation:

Symbolically, your math problem reads:

1 1

-------- = --------

p^5 243

We need only solve p^5 = 243 to obtain p.

Note that p^5 = 243.

You're not really expected to memorize 5th powers (tho' it's nice if you can).

Instead, factor 243; we get 3(81), or 3(3)(27). Note that 3(3)(27) = 3(3^1)(3^3). Identify and add together all the exponents of p here: 1+1+3 = 5. This tells us that 243 = 3^5.

Thus, p^5 = 243, and p = 3.