Question

What can $(5^2{)}^3$ be expressed as:

• A. $5^6$
• B. $5^5$
• C. $5^8$
• D. $5^9$

Answer 1

The correct option is A $5^6$

$(5^2{)}^3$ can be written as,
$(5^2{)}^3=5^2\times 5^2\times 5^2$

Since the exponents $2$ have the same base $5$, we can further write as,
$(5^2{)}^3=5^2\times 5^2\times 5^2$
$=5^{(2+2+2)}$ $(\because a^m\times a^n\times a^p=a^{m+n+p})$
$=5^6$
Alternate solution:
$\because (a^m{)}^n=a^{mn}$
$\Rightarrow (5^2{)}^3=5^{2\times 3}=5^6$