Question

Simplify and express the result in power notation with positive exponent.
(3^-7÷3^-9)×3-4​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Simplify:

• (3^-7÷3^-9)×3^-4

Solution:

$\implies \dfrac{3^{-7}}{3^{-9}} \times 3^{-4} \\ \\ \implies 3^{-7 - (-9) + (-4)} \\ \\ \implies 3^{-7 + 9 - 4} \\ \\ \implies 3^{-2} \\ \\ \bold {\implies \dfrac{1}{3^2}}$

Concept Used:

• $a^m \times a^n = a^{m+n}$
• $\dfrac{a^m}{a^n} = a^{m-n}$

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$