Question

fill in the blank 1 point
\\(\frac{11^{-7} \cdot 5^{9}}{6^{-9}}\\) = answer
options (from image):
\\(5^{9}/(11^{7} \cdot 6^{9})\\), \\(21^{4}/8^{6}\\), \\(6^{9}/(11^{7} \cdot 5^{9})\\), \\(8/21^{3}\\), \\(16^{3}/(-7)^{3}\\), \\(7^{3}/16^{9}\\), \\((6^{9} \cdot 5^{9})/11^{7}\\), \\((3^{5} \cdot 21^{4})/(7^{9} \cdot (-4)^{19})\\), \\((6^{9} \cdot 5^{9})/11^{7}\\), \\(1/(8 \cdot 21)^{4}\\), \\((7^{5} \cdot (-4)^{7})/(3^{5} \cdot (-21)^{4})\\), \\(16^{3}/7^{3}\\), \\((3^{5} \cdot 7^{7})/(-21)^{4}\\)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$, so:
$$\frac{11^{-7} \cdot 5^9}{6^{-9}} = \frac{5^9 \cdot 6^9}{11^7}$$

Step2: Rearrange the expression

Group the terms in the numerator:
$$\frac{6^9 \cdot 5^9}{11^7}$$

Answer:

$\boldsymbol{\frac{(6^9 \cdot 5^9)}{11^7}}$ (matches the option $\vdots\vdots(6^9\cdot5^9)/11^7$)