Question

If $40000=2^{\text{a}}\times 5^{\text{b}}$, then the respective values of $\text{a}$ and $\text{b}$ are:

• A. $4$ and $6$
• B. $6$ and $4$
• C. $6$ and $6$
• D. $4$ and $4$

Answer 1

The correct option is B $6$ and $4$

Expressing $40000$ in terms of prime factors $2$ and $5$, we get:

$40000=2\times 2\times 2\times 2\times 2\times 2\times 5$$\times 5\times 5\times 5=2^6\times 5^4$

Now, comparing the value of $2^6\times 5^4$ with $2^{\text{a}}\times 5^{\text{b}}$, we get the required values are $\text{a}=6$ and $\text{b}=4$.