Question

Evaluate $\frac{a^3\times a^5}{(a^3{)}^2}$.

• A. $a^4$
  
• B. $a^3$
  
• C. $a^2$
  
• D. $a^5$
  

Answer 1

The correct option is C $a^2$


Given: $\frac{a^3\times a^5}{(a^3{)}^2}$
By the Laws of Exponents, we know that $a^m\times a^n=a^{m+n}$
and $(a^m{)}^n=a^{mn}$
$⟹$ $\frac{a^3\times a^5}{(a^3{)}^2}=\frac{a^{3+5}}{a^{3\times 2}}=\frac{a^8}{a^6}$
We know that, $\frac{a^m}{a^n}=a^{m-n}$
$⟹$$\frac{a^8}{a^6}=a^{8-6}=a^2$