Question

Solve the following using laws of exponents and arrange them in ascending order.

• A. ${10}^4÷{10}^2$
• B. ${10}^3\times {10}^2$
• C. ${10}^8÷{10}^2$
• D. ${10}^3\times {10}^7$

Answer 1

${10}^4÷{10}^2$:
$\because a^m÷a^n$ = $a^{m-n}$
$\therefore {10}^4÷{10}^2$ = ${10}^{4-2}$
= ${10}^2$

${10}^3\times {10}^2$:
$\because a^m\times a^n$ = $a^{m+n}$
$\therefore {10}^3\times {10}^2$ = ${10}^{3+2}$
= ${10}^5$

${10}^8÷{10}^2$:
$\because a^m÷a^n$ = $a^{m-n}$
$\therefore {10}^8÷{10}^2$ = ${10}^{8-2}$
= ${10}^6$

${10}^3\times {10}^7$:
$\because a^m\times a^n$ = $a^{m+n}$
$\therefore {10}^3\times {10}^7$ = ${10}^{3+7}$
= ${10}^{10}$

So, the ascending order is: ${10}^2<{10}^5<{10}^6<{10}^{10}$
$\Rightarrow {10}^4÷{10}^2<{10}^3\times {10}^2<{10}^8÷{10}^2<{10}^3\times {10}^7$