Question

Drag values to complete each equation.

Answer 1

Answer:

$9^{-7}$ and $9^{-2}$

Step-by-step explanation:

using the rules of exponents

• $(a^m)^{n}$ = $a^{mn}$

• $a^{m}$ × $a^{n}$ = $a^{(m+n)}$

• $\frac{a^{m} }{a^{n} }$ = $a^{(m-n)}$

given ($9^{5}$ × $9^{-9}$ ) / $9^{3}$

= $\frac{9^{5+(-9)} }{9^{3} }$ = $\frac{9^{-4} }{9^{3} }$ = $9^{-4-3}$ = $9^{-7}$

given $(9^4)^{3}$ × $9^{-14}$

= $9^{12}$ × $9^{-14}$

= $9^{12+(-14)}$ = $9^{-2}$

Answer 2

Answer:  The required values of the given expressions are

$\dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.$

Step-by-step explanation:  We are given to find the values of the following expressions :

$E_1=\dfrac{9^5.9^{-9}}{9^3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=(9^4)^3.9^{-14}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We will be using the following properties of exponents :

$(i)~x^a.x^b=x^{a+b},\\\\(ii)~\dfrac{x^a}{x^b}=x^{a-b}\\\\(iii)~(x^a)^b=x^{ab}.$

From expression (i), we get

$E_1\\\\\\=\dfrac{9^5.9^{-9}}{9^3}\\\\\\=\dfrac{9^{5+(-9)}}{9^3}\\\\\\=\dfrac{9^{-4}}{9^3}\\\\\\=9^{-4-3}\\\\=9^{-7}$

and from expression (ii), we get

$(9^4)^3.9^{-14}\\\\=9^{4\times3}.9^{-14}\\\\=9^{12}.9^{-14}\\\\=9^{12+(-14)}\\\\=9^{-2}.$

Thus, the required values of the given expressions are

$\dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.$