Question

fill in the blank 1 point
\\(\frac{11^{-7} \cdot 5^9}{6^9} = \\)
answer
options (from image):
\\(6^9 / (11^7 \cdot 5^9)\\)
\\(7^3 / 16^9\\)
\\(21^4 / 8^6\\)
\\(8 / 21^3\\)
\\(16^3 / 7^3\\)
\\(1 / (8 \cdot 21)^4\\)
\\((3^5 \cdot 21^4) / (7^9 \cdot (-4)^{10})\\)
\\((3^5 \cdot 7^7) / (-21)^4\\)
\\((6^9 \cdot 5^9) / 11^7\\)
\\((7^5 \cdot (-4)^7) / (3^5 \cdot (-21)^4)\\)
\\(16^3 / (-7)^3\\)
\\(5^9 / (11^7 \cdot 6^9)\\)
\\(5^9 / (11^7 \cdot 6^9)\\)

Explanation:

Step1: Rewrite negative exponent

$11^{-7} = \frac{1}{11^7}$

Step2: Substitute into original expression

$\frac{\frac{1}{11^7} \cdot 5^9}{6^9} = \frac{5^9}{11^7 \cdot 6^9}$

Answer:

$\frac{5^9}{11^7 \cdot 6^9}$