Can someone solve this

[onedayi'll]

(10^100)^10^100 = 10^k, what is the value of k?

^ -> power of.

[hk_4u]

Two interpretations

1 -
((A^B)^C)^D = A^BCD

so

(10^100)^10^100 = 10^k

10^100000 = 10^k

k = 100000

2 - (A^B)^C^D = A^(B^C^D)

so
(10^100)^10^100 = 10^k

10^(100^10^100) = 10^k

k = (100^10^100)

[truplayer256]

(10^100)^(10^100)=10^k

Remember that we multiply exponents when they're raised to a power.

k=100*10^100=10^2*10^100=10^102

[sadullaevd]

(10^100)^(10^100)=10^k

Remember that we multiply exponents when they're raised to a power.

k=100*10^100=10^2*10^100=10^102

Seems typo, could you the bold part plz,

IMO should k= 100*10*100= 100 000 (instead of ^ should be *)

cheers,

[truplayer256]

Why should k be 100*100*100, sadullaevd? I think you're making a common error.

10^100 quantity is being raised to 10^100 so it should equal 10^(100*10^100)=10^(102). As a result, k should equal 10^(102)

[sadullaevd]

my bad, it should be 10^102

misinterpreted the question,

thx,

cheers,