Question

Find the value of $\frac{5^5}{{10}^5}$.

• A. $\frac{1}{32}$
  
• B. $\frac{1}{16}$
  
• C. $\frac{1}{8}$
  
• D. $32$
• E. $16$

Answer 1

The correct option is A $\frac{1}{32}$


This is of the form $\frac{a^m}{b^m}={\left(\frac{a}{b}\right)}^m$ where $a,b$ are different bases.
Hence, $\frac{5^5}{{10}^5}={\left(\frac{5}{10}\right)}^5$
$={\left(\frac{1}{2}\right)}^5$
$=\frac{1}{2^5}$
$=\frac{1}{32}$