Question

using the laws of exponents, simplify and write the answer in exponential form: 1.) 8 raised to the power t divided by 8 raised to the power 2.​

Answer 1

$\frac{8^t}{8^2} =8^{t-2}\:--\:[Using\:Division\:rule\:of\:exponents, \:\frac{a^m}{a^n}=a^{m-n} ]$

Or, to be more rigorous,

$\frac{8^t}{8^2}=8^t\times\frac{1}{8^2} =8^t\times8^{-2}\:--\:[Using\:negative\:exponent\:rule,\frac{1}{a^x}= a^{-x}]\\=8^{t+(-2)}\:--\:[Using\:multiplication\:rule,a^m\times a^n=a^{m+n}]\\=8^{t-2}$