Question

Mhhhh, I dont think i can ever finish these questions because I am new to this chapter...

Find the missing numbers​
now its a bit clear

Answer 1

Answer:

$let \: take \: the \: missing \:number = n \\ a) : {4}^{n} \times {4}^{6} = {4}^{ - 2} \\ {4}^{n + 6} = {4}^{ - 2} \\\blue{\mathfrak{\underline{\large{now \: compare}}}:} \\ n + 6 = - 2 \\ \boxed{n = - 8} \\ b) : { ({7}^{3} )}^{2} = {7}^{n} \\ {7}^{6} = {7}^{n} \\\blue{\mathfrak{\underline{\large{now \: compare}}}:} \\ 6 = n\\ \boxed{n = 6} \\ c) : {4}^{3} \times {2}^{7} = {4}^{n} \\ {( {2}^{2} )}^{3} \times {2}^{7} = {( {2}^{2}) }^{n} \\ {2}^{6} \times {2}^{7} = {2}^{2n} \\ {2}^{6 + 7} = {2}^{2n} \\ {2}^{13} = {2}^{2n} \\\blue{\mathfrak{\underline{\large{now \: compare}}}:} \\ 13 = 2n \\ \boxed{n = \frac{13}{2} } \\ d) : {3}^{ - 8} \div {9}^{n} = {3}^{ - 12} \\ {3}^{ - 8} \div {3}^{2n} = {3}^{ - 12} \\ {3}^{ - 8 - 2n} = {3}^{ - 12} \\\blue{\mathfrak{\underline{\large{now \: compare}}}:} \\ - 8 - 2n = - 12 \\ - 2n = - 4 \\ \boxed{n = 2} \\ \\\red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$