BTGmoderatorDC wrote:If n = 10^10 and n^n = 10^d, what is the value of d?
A. 10^3
B. 10^10
C. 10^11
D. 10^20
E. 10^100
Substituting n= 10¹� into n^n = 10^d, we get:
(10
¹� )^(
10¹�)= 10^d
When an exponent is raised to a power, we MULTIPLY the exponents.
Multiplying the exponents in blue, we get:
10^(
10*10¹�) = 10^d
10^(
10¹¹) = 10^
d
Since each side has the same base, the exponent in blue must be equal to the exponent in red:
10¹¹ =
d.
The correct answer is
C.
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