Question

The exponential form of 512 is ${2}^{k}$ then the value of k is ___.

Answer 1

Hint: Find the prime factors of 512. Then by equating it with ${2}^{k}$ , deduce the value of k. Exponents simply refer to how many times a particular number appears in a numerical term.

Complete step-by-step answer:
We will find the prime factors of 512 is.

2	512
2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

 The prime factors are: \[2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
 = $2^9$.
Therefore, the exponential form of 512 = $2^9$ .
From the question,
Exponential form of 512 = $2^k$
\[ \Rightarrow \] $2^k$ = $2^9$
\[ \Rightarrow \]k = 9 (Same base equalises the power)
Therefore, the required answer k = 9.
Note: In this type of question, find prime factors first and then using the property of exponent (base is same, then power will be equal) . We can easily find the value of k.