Question

simplify. write the answer using positive exponents only.\\(\frac{6^{-3}x^{9}y^{9}}{x^{-10}y^{-9}}\\)\\(\frac{6^{-3}x^{9}y^{9}}{x^{-10}y^{-9}}=\square\\)\\((\text{use integers or fractions for any numbers in the expression.})\\)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$ and $\frac{1}{a^{-n}}=a^n$.
$\frac{6^{-3}x^{9}y^{9}}{x^{-10}y^{-9}} = 6^{-3} \cdot x^{9-(-10)} \cdot y^{9-(-9)}$

Step2: Simplify exponents of variables

Calculate the exponents for $x$ and $y$.
$6^{-3} \cdot x^{19} \cdot y^{18}$

Step3: Rewrite $6^{-3}$ as positive exponent

Convert the constant term to positive exponent.
$6^{-3} = \frac{1}{6^3} = \frac{1}{216}$

Step4: Combine all terms

Multiply the constant with variable terms.
$\frac{x^{19}y^{18}}{216}$

Answer:

$\frac{x^{19}y^{18}}{216}$