Question

If ${\left(5\right)}^{a+b}=5\times 25\times 125$, what is the value of ${(a+b)}^2$ ?

• A. $25$
• B. $28$
• C. $36$
• D. $44$

Answer 1

Answer: (C)

$36$

$5^{a+b}=5\times 25\times 125=5\times 5^2\times 5^3=5^{1+2+3}=5^6$

Equating exponents $a+b=6$

$\therefore (a+b{)}^2=6^2=36$