Question

What is the value of $a$ that satisfies the equation $2^5\times 4^5=2^a$?

• A. 5
• B. 10
• C. 12
• D. 15

Answer 1

The correct option is D 15

$2^5\times 4^5$
$={(2\times 4)}^5(\because a^m\times b^m=(ab{)}^m)=8^5=(2^3{)}^5=2^{3\times 5}(\because (a^m{)}^n=a^{mn})=2^{15}$
Since $2^5\times 4^5=2^a=2^{15},$ we have $a=15.$