Question

please answer this question​

Answer 1

$\huge\fcolorbox{cyan}{orange}{Solutions:-}$

$11.i) {4}^{5} \times {4}^{2} \times {4}^{4} \\ = > ( { {2}^{2}) }^{5} \times ({ {2}^{2} )}^{2} \times( { {2}^{2} )}^{4} \\ = > {2}^{10} \times {2}^{4} \times {2}^{8} \\ = > {2}^{10 + 4 + 8} \\ = > {2}^{22} (ans)$

$11.ii) {( {3}^{2} \times {3}^{3} )}^{7} \\ = > ( { {3}^{2}) }^{7} \times ({ {3}^{3} )}^{7} \\ = > {3}^{14} \times {3}^{21} \\ = > {3}^{14 + 21} \\ = {3}^{35} (ans)$

$\fbox\pink{\fbox\orange{Formula:-}}$

$i)=>{a}^{b} \\ = > a \: is \: base \\ = > b \: is \: the \: power \:.$

$ii){a}^{b} \times {a}^{c} \times {a}^{d} \\ = > {a}^{b + c + d}$

So, from the above rule we can conclude that in Multiplication if the base is same then we can add all the powers.

$iii)({{a}^{b})}^{c} = {a}^{bc}$