Question

What is the value of 5 to the power of 4 over 5 to the power of 6?

Answer 1

$\dfrac{5^4}{5^6}=\dfrac{5\cdot5\cdot5\cdot5}{5\cdot5\cdot5\cdot5\cdot5\cdot5}\\\\=\dfrac{\not5\cdot\not5\cdot\not5\cdot\not5}{\not5\cdot\not5\cdot\not5\cdot\not5\cdot5\cdot5}=\dfrac{1}{5\cdot5}=\dfrac{1}{25}$

$Use:\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n}\\\\\dfrac{5^4}{5^6}=5^{4-6}=5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{25}$