Question

Sort the following numbers in increasing order from top to bottom.

• A. $2^5\times 5^2$
• B. $2^2\times 5^2$
• C. $2^3\times 5^3$
• D. $5^1\times 2^5$

Answer 1

$2^5\times 5^2$=$(2\times 2\times 2\times 2\times 2)\times (5\times 5)$
On rearranging the above equation,
$=(2\times 5)\times (2\times 5)\times (2\times 2\times 2)$
$=(10\times 10)\times 8$
$=100\times 8$
$=800$

$2^2\times 5^2$=$(2\times 2)\times (5\times 5)$
On rearranging the above equation,
$=(2\times 5)\times (2\times 5)$
$=(10\times 10)$
$=100$

$2^3\times 5^3$=$(2\times 2\times 2)\times (5\times 5\times 5)$
On rearranging the above equation,
$=(2\times 5)\times (2\times 5)\times (2\times 5)$
$=(10\times 10\times 10)$
$=1000$

$5^1\times 2^5$=$\left(5\right)\times (2\times 2\times 2\times 2\times 2)$
On rearranging the above equation,
$=(2\times 5)\times (2\times 2\times 2\times 2)$
$=(10\times 16)$
$=160$