#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, pair& p){return is >> p.first >> p.second;} template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const pair& p){return os << p.first << " " << p.second;} template ostream& operator << (ostream& os, const vector& vec){for(size_t i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(size_t i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; using real = double;//long double; double calc(real a, real b, real lgt, real init_x){ auto f = [&](real x){ real lgx = log(x); return a*lgx + b*log(lgx) - lgt; }; auto f_ = [&](real x){ real lgx = log(x); return (a*lgx + b) / (x*lgx); }; real x = init_x; for(int t=0; t<25; t++){ x = x - f(x) / f_(x); } return x; } //double calc2(real a, real lgt, real init_x){ // auto f = [&](real x){ // real lgx = log(x); // return a*lgx - lgt; // }; // auto f_ = [&](real x){ // return a/x; // }; // auto g = [&](real x){ // return x * (a * log(x) - lgt) / a; // }; // real x = init_x; // for(int t=0; t<25; t++){ // x = x - g(x);//f(x) / f_(x); // } //return x; //} double calc3(real b, real lgt, real init_x){ // auto f = [&](real x){ // return b*log(log(x)) - lgt; // }; // auto f_ = [&](real x){ // return b/(x*log(x)); // }; auto g = [&](real x){ real lgx = log(x); return x * lgx * (b * log(lgx) - lgt) / b; }; real x = init_x; for(int t=0; t<14; t++){ x = x - g(x);//f(x) / f_(x); } return x; } int main(){ int n; scanf("%d", &n); while(n--){ double a,b,t; scanf("%lf%lf%lf", &a,&b,&t); real x = 1.1; real lgt = log(t); double ans; if(b<0.1){ // ans = calc2(a,t,x); // while(isnan(ans)){ // x *= 1.5; // //if(x<1.0) x += 11.4514; // ans = calc2(a,lgt,x); // } ans = pow(t, 1.0/a); }else if(a<0.1){ // ans = calc3(b,lgt,x); // while(isnan(ans)){ // x *= 1.5; // //if(x<1.0) x += 11.4514; // ans = calc3(b,lgt,x); // } ans = exp(pow(t, 1.0/b)); }else{ ans = calc(a,b,lgt, x); while(isnan(ans)){ x *= 0.995; ans = calc(a,b,lgt, x); } } assert(isnan(ans) == false); printf("%.22f\n", ans); } return 0; }