Question

fill in the blank 1 point
\\(\frac{8^{-4}}{21^{-4}}\\) = answer
options: \\(6^9/(11^7\cdot5^9)\\), \\(1/(8\cdot21)^4\\), \\(8/21^3\\), \\(16^3/7^2\\), \\((6^9\cdot5^9)/11^7\\), \\((3^5\cdot7^2)/(-21)^4\\), \\(21^4/8^6\\), \\((7^5\cdot(-4)^7)/(3^5\cdot(-21)^4)\\), \\(21^4/8^6\\), \\(16^3/(-7)^2\\), \\((3^5\cdot21^4)/(7^9\cdot(-4)^{10})\\), \\(7^3/16^9\\), \\(5^9/(11^7\cdot6^9)\\)

Explanation:

Step1: Rewrite negative exponents

Recall $x^{-n}=\frac{1}{x^n}$, so $\frac{8^{-4}}{21^{-4}}=\frac{\frac{1}{8^4}}{\frac{1}{21^4}}$

Step2: Divide by reciprocal

Dividing by a fraction is multiplying by its reciprocal: $\frac{1}{8^4} \times 21^4 = \frac{21^4}{8^4}$

Answer:

$\frac{21^4}{8^4}$