Question

simplify : (3rase to the power - 7 ÷3rase to the power-9)multiply 3 rase to the power - 4​

Answer 1

Answer:

$\frac{1}{9}$

Step-by-step explanation:

Question states:

Simplify $(\frac{3^{-7} }{3^{-9}}) *3^{-4}$

We know that $\frac{a^{m} }{a^{n} } = a^{m-n}$

⇒ $3^{-7-(-9)} *3^{-4}$

⇒ $3^{-7+9} *3^{-4}$

⇒ $3^{2} *3^{-4}$

We know that $a^{m} *a^{n} = a^{m+n}$

⇒ $3^{2 + (-4)}$

⇒ $3^{2-4}$

⇒ $3^{-2}$

We know that $a^{-m} = \frac{1}{a^{m} }$

⇒ $\frac{1}{3^{2} }$

⇒ $\frac{1}{9}$