Question

Which expressions are equivalent to 5^12*5^8? Choose 2 answers:

Answer 1

${5}^{12} \times {5}^{8} \\ = {5}^{12 + 8} \\ = {5}^{20}$

Therefore,

$a) \: {25}^{20} ≠ {5}^{20}$

$b) ({25}^{5} ) ^{4} \\ = {25}^{5 \times 4} \\ = {25}^{20} \\ ( {25}^{5} )^{4} ≠ {5}^{20}$

$c) \: ( {5}^{3} . {5}^{2} ) ^{4} \\ = ({5}^{3 + 2}) ^{4} \\ = ({5}^{5} )^{4} \\ = {5}^{20}$

$d) \: {(5 ^{5}) }^{4} \\ = {5}^{5 \times 4} \\ = {5}^{20}$

Answers:

$c)( {5}^{3} . {5}^{2} {)}^{4} \\ d) {(5}^{5} ) ^{4}$

Hope you could understand.

If you have any query, feel free to ask.