Free Exponents and Powers 03 Practice Test - 7th grade 

343 can be written as

$343=7\times 7\times 7$
so, $343=7^3$

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, $8\times 9=72$

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

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

$21700000$ can be written as

$2.17\times 10000000=2.17\times {10}^7$

Expanding the terms:

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

From the law of exponent, we have,

$(a^m{)}^n=(a{)}^{mn}$
Therefore,
$({10}^2{)}^2={10}^4=10000$ 

Here, 4 is called the exponent.

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

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

Hence, the given statement is false.

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