Question

question 10
5 pts
perform the indicated operations. write the result using only positive exponents. assume all variables represent nonzero real numbers.
\\(\frac{3x^{-3}}{9x^{-9}}\\)
\\(\frac{x^6}{3}\\)
\\(\frac{x^6}{6}\\)
\\(\frac{x^3}{3}\\)
\\(\frac{x^{12}}{3}\\)
question 11
5 pts
perform the indicated operations. write the result using only positive exponents. assume all variables represent nonzero real numbers.
\\(\frac{x^4}{x^{-7}}\\)

Explanation:

For Question 10:

Step1: Simplify coefficient fraction

$\frac{3}{9} = \frac{1}{3}$

Step2: Apply exponent quotient rule

$x^{-3 - (-9)} = x^{6}$

Step3: Combine coefficient and variable

$\frac{1}{3} \times x^6 = \frac{x^6}{3}$

Step1: Apply exponent quotient rule

$x^{4 - (-7)} = x^{4+7}$

Step2: Calculate exponent sum

$x^{11}$

Answer:

$\frac{x^6}{3}$

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For Question 11: