Question

Which of the following option is equal to $8^5?$

• A. $2^8$
• B. $5^8$
• C. $2^{15}$
• D. None of the above

Answer 1

The correct option is C $2^{15}$

$\underset{–}{\text{Need to simplify:}}{8}^5$

$8^5$
$=(2^3{)}^5$ $[\because 8=2\times 2\times 2=2^3]$

$=2^{3\times 5}=2^{15}$
$[\because$ Repeated exponentiation: $(a^m{)}^n=a^{m\times n}]$

Therefore, option (c.) is the correct one.