Simplify fully

Question

X^-1.8^r+2. 4^-3r /2^-2r

Answer 1

First, let's simplify the expression step by step.

1. X^-1.8^r+2

This can be rewritten as X^(-1.8r + 2).

2. 4^-3r

This can be rewritten as (1/4)^(3r).

3. 4^-3r / 2^-2r

This can be rewritten as (1/4)^(3r) / 2^(-2r).

Now, let's substitute the expressions in step 1 and step 2 into the expression in step 3:

(X^(-1.8r + 2)) * ((1/4)^(3r)) / (2^(-2r))

Now, let's simplify further:

= X^(-1.8r + 2) * 1/(4^(3r)) / 1/(2^(-2r))

= X^(-1.8r + 2) * 1/(4^(3r)) * (2^(2r))

= X^(-1.8r + 2) * (2^(2r)) / (4^(3r))

= X^(-1.8r + 2) * (2^(2r)) / (2^(6r))

Since the bases of the numerator and denominator are the same, we can subtract the exponents:

= X^(-1.8r + 2 - 6r)

= X^(-6.8r + 2)

Therefore, the simplified expression is X^(-6.8r + 2).