Помогите действие со ступенями формат егэ. 1) 5^0.36 ·25^0.32 2)4^3.5·5^2.5/20^1.5...

Question

Помогите действие со ступенями формат егэ. 1) 5^0.36 ·25^0.32 2)4^3.5·5^2.5/20^1.5 3)8^0.76·64^0.12 4)4·10^3+5·10^2+6·10^1

Answer 1

5^0.36·25^0.32=5^0.36·5^0.64=5^(0.36+0.64)=5^1=5
4^3.5·5^2.5/20^1.5=4^3.5·5^2.5/(4^1.5·5^1.5)=4^(3.5-1.5)·5^(2.5-1.5)=4^2·5^1=16·5=80
8^0.76·64^0.12=8^0.76·8^0.24=8^(0.76+0.24)=8^1=8
4·10^3+5·10^2+6·10^1=4000+500+60=4560

Answer 2

1)5^0.36*25^0.32
5^0.36*(5²)^0.32
5^0.36*5^0.64 = 5

 2)4^3.5·5^2.5/20^1.5
(2²)^7/2*5^(0.125^3/2)
2^7*5((1/8)^3/2)
125*5√(1/8)³
128*5^1/8*√1/8
125*5^1/8*1/√8
128*5^1/8*1/2√2
128*5^√2/32 ≈ 137.43

3)8^0.76·64^0.12 
(2³)^0.76*(2^6)^0.12
2^2.28*2^0.72
2³=8

4)4·10^3+5·10^2+6·10^1
4*10³+5*10²+6*10
10(4*100+50+6)
10(400+50+6)
10*456 = 4560