Question

2. Simplify:

(v) (3^-7 ÷ 3^10) * 3^-5

Answer 1

Hey mate!!!!

$( {3}^{ - 7} \div {3}^{ 10} ) \times {3}^{ - 5}$
=
$({3}^{ - 7 - 10)} ) \times {3}^{ - 5}$
we know that exponents which are on the same base and are being divided, are subtracted.
=>
$({3}^{ - 7 - 10} ) \times {3}^{ - 5}$
=
${3}^{-17} \times {3}^{ - 5}$
now we can add -17 and -5
=
${3}^{-17 + ( - 5)} \\ = 3 {}^{-17 - 5} \\ = {3}^{ - 22} = \frac{1}{3 {}^{22} }$

3-²²

Hope it helps dear friend ☺️✌️

Answer 2

hiii!!!

here's Ur answer...

first of all, lemme tell u some laws of exponents which are used in this equation.

(i) a^m × a^n = a^m+n

(ii) a^m ÷ a^n = a^m-n

(iii) (a/b)^-m = (b/a)^m

now, let's solve it..

$given \: = > \frac{ {3}^{- 7} }{ {3}^{10} } \times {3}^{ - 5} \\ \\ = ( {3}^{ - 7 - 10} ) \times {3}^{ - 5} \\ \\ = {3}^{ - 17} \times {3}^{ - 5} \\ \\ = {3}^{ - 17 + ( - 5)} \\ \\ = {3}^{ - 17 - 5} \\ \\ = {3}^{ - 22}$
= 1/(3)²²

hope this helps..!!