Let k = 10^10. What is k^k equal to in terms of zeros?

To determine what ( k^k ) equals in terms of zeros when ( k = 10^{10} ), we can break down the expression as follows:

1. Substitute ( k ) into the expression:

[

k^k = (10^{10})^{10^{10}}

]

2. Apply the power of a power property:

[

(a^m)^n = a^{m \cdot n}

]

Here, ( a = 10 ), ( m = 10 ), and ( n = 10^{10} ). Therefore:

[

(10^{10})^{10^{10}} = 10^{10 \cdot 10^{10}}

]

3. Calculate the exponent:

[

10 \cdot 10^{10} = 10^1 \cdot 10^{10} = 10^{1 + 10} = 10^{11}

]

4. Thus, we rewrite the expression:

[

k^k = 10^{10^{11}}

]

This means that the number of zeros in ( k^k \