Question

Arrange in ascending order.

$2^5,3^3,2^3\times 2,(3^3{)}^2,3^5,4^0,2^3\times 3^1$

Answer 1

In ascending order, the numbers are arranged from smallest to largest.
We have,
$2^5=2\times 2\times 2\times 2\times 2=32$
$3^3=3\times 3\times 3=27$
$2^3\times 2=2\times 2\times 2\times 2=16$
$(3^3{)}^2=3^{3\times 2}=3^6=3\times 3\times 3\times 3\times 3\times 3=729$
$3^5=3\times 3\times 3\times 3\times 3=243$
$4^0=1$
$2^3\times 3^1=2\times 2\times 2\times 3=24$

$1<16<24<27<32<243<729$

Thus, the required ascending order will be
$4^0<2^3\times 2<2^3\times 3^1<3^3<2^5<3^5<(3^3{)}^2.$