Question

question 21
write the expression with positive exponents, then simplify, if possible.
$3^{-2} + 3^{-2} = $
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question 22
use properties of exponents to simplify the expression. write all answers with positive exponents only. (assume all variables are nonzero.)
$\frac{x^{-2}}{x^{8}} = $
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Explanation:

Step1: Rewrite with positive exponents

$3^{-2} = \frac{1}{3^2} = \frac{1}{9}$, so $3^{-2} + 3^{-2} = \frac{1}{9} + \frac{1}{9}$

Step2: Add the fractions

$\frac{1}{9} + \frac{1}{9} = \frac{1+1}{9} = \frac{2}{9}$

Step3: Apply exponent subtraction rule

For $\frac{x^{-2}}{x^8}$, use $\frac{x^a}{x^b}=x^{a-b}$: $x^{-2-8}=x^{-10}$

Step4: Rewrite with positive exponent

$x^{-10} = \frac{1}{x^{10}}$

Answer:

Question 21: $\frac{2}{9}$
Question 22: $\frac{1}{x^{10}}$