Question

Express x ^ - 2 + 27 ^ x in simplest form when x = 2/3

Answer 1

45/4

Explanation:

You want to know the value of x^-2 +27^x when x=2/3.

Evaluation

A calculator or spreadsheet can evaluate this expression for you.

The "by hand" evaluation can look like this:

`\left((2)/(3)\right)^(-2)+27^(2/3)=(3^2)/(2^2)+(3^3)^(2/3)=(3^2)((1)/(4)+1)\\\\=9\cdot(5)/(4)=\boxed{(45)/(4)}`

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Additional comment

The applicable rules of exponents are ...

a^-b = 1/a^b

(a^b)^c = a^(bc)