32000 can be written as
$32000=(2\times 2\times 2\times 2\times 2)\times 1000=2^5\times {10}^3$
$(as32=2\times 2\times 2\times 2\times 2)$

= $2^5\times (2\times 2\times 2\times 5\times 5\times 5)$
= $2^5\times 2^3\times 5^3$
= $2^8\times 5^3$

Putting $a=2andb=3$
We get:
$2^3=2\times 2\times 2=8and{3}^2=9$ 
Hence, $8\times 9=72$

$21700000$ can be written as
$2.17\times 10000000=2.17\times {10}^7$

Here the two terms have  $3^3$ and $3^2$ have different exponents, but the same base.Hence by adding the powers  we get,

$3^3\times 3^2=3^{3+2}$ = $3^5=243$

Expanding the terms:

$(3\times 2{)}^3=6^3=216$

From the law of exponents, we know that
$a^m\times b^m=(ab{)}^m$
Thus, the given statement is true.

$\frac{2^2}{5^2}$ = $\frac{4}{25}$

$-\frac{2^2}{5^2}$ = $-\frac{4}{25}$

Hence, the given statement is false.

Steps: 1 Mark
Answer: 1 Mark
The prime factorisation of 726 and 938 are given below.
$726=\left(2\right)\times \left(3\right)\times \left(11\right)\times \left(11\right)$
$\Rightarrow 726=2^1\times 3^1\times {11}^2$
$938=\left(2\right)\times \left(7\right)\times \left(67\right)$
$\Rightarrow 938=2^1\times 7^1\times 67$
Both have the same powers of 2 which is 1.

$625=\left(5\right)\times \left(5\right)\times \left(5\right)\times \left(5\right)$
$\Rightarrow 625=5^4$

Concept: 1 Mark
Answer: 1 Mark
Here we know that for any non zero number if the base is same and the number is multiplied, then the exponents are added.
$\left(8\right)\times \left(8\right)\times \left(8\right)\times \left(8\right)\times \left(8\right)$
$=2^3\times 2^3\times 2^3\times 2^3\times 2^3$
$=2^{3+3+3+3+3}$
$\because a^b\times a^c=a^{b+c}$
$=2^{15}$