Question

If
${2}^{ {b}^{a} } - {2}^{ {a}^{b} } = {2}^{115 } ( {2}^{ {2}^{c} } - {2}^{10} )$
,where a, b and c are odd prime numbers less than 10, then find the value of
$\frac{ {a}^{b} }{ {a}^{c} } .$

step by step explanation will be given brainlist answer...... ​

Answer 1

Explanation:

ab+4=dc....(1)

ba+40=dc....(2)

a,c→ neither prime nor composite a=c=1

b,d prime</div><div>from(1)</div><div>b+10(a)+4=c(10)+d</div><div>\Rightarrowb+10(1)+4=1(10)+d</div><div>\Rightarrowb+4=d....(1)</div><div>From(2)</div><div>10(b)+a+40=10(d)+c</div><div>\Rightarrow10b+1+40=10d+1</div><div>\Rightarrow40=10(d-b)</div><div>andbanddareprime</div><div>\Rightarrowb=3andd=7(o<span>nlypossibility)</span></div><div><span>\cfrac{ab+ba}{cd+dc}=\cfrac{13+31}{17+71}=\cfrac{44}{88}=\cfrac{1}{2}$$