Question

Match the first column elements with their correct answers given in the second column:

• A. $3^{10}$
• B. $3^8$
• C. $3^7$
• D. $3^{12}$

Answer 1

$\underset{–}{\text{Note:}}\frac{a^m}{a^n}=a^{m-n}$, $(a^m{)}^n=a^{m\times n}$ and $a^0=1$

$\bullet \frac{{81}^5}{{81}^3}=(81{)}^{5-3}=(81{)}^2=(3^4{)}^2=3^{4\times 2}=3^8$

$\bullet \frac{{27}^6}{{27}^2}=(27{)}^{6-2}$
$=(27{)}^4$
$=(3^3{)}^4$
$=3^{3\times 4}$
$=3^{12}$

$\bullet \frac{9^9}{9^4}=9^{9-4}$
$=9^5=(3^2{)}^5$
$=3^{2\times 5}$
$=3^{10}$

$\bullet \frac{3^7}{1}=\frac{3^7}{3^0}=3^{7-0}=3^7$