Question

Efectuati calculele urmatoare,utilizand regulile de calcul puteri:
A)(√2)^3*(√2)^4:(√2)^5=
B)(√3/4)^12:(√3/4)^7:(√3/4)^4*(√3/4)=
C)[(2/3)^4]^5*[(2/3)^3]^4:[(2/3)^5]^4=
D)(√7/25)^12*(-25/√7)^12=
Dau coroana primului raspuns corect.

Answer 1

A)(√2)³x(√2)⁴:(√2)⁵=(√2)³⁺⁴⁻⁵=√2²=2

B)(√3/4)¹²:(√3/4)⁷:(√3/4)⁴x(√3/4)=(√3/4)¹²⁻⁷⁻⁴⁺¹=(√3/4)²=3/4

C)[(2/3)⁴]⁵x[(2/3)³]⁴:[(2/3)⁵]⁴=(2/3)²⁰x(2/3)¹²:(2/3)²⁰=(2/3)²⁰⁺¹²⁻²⁰=(2/3)¹²

D)(√7/25)¹²x(-25/√7)¹²=se simplifica=1¹²x(-1)¹²=1x1=1

Answer 2

 [tex]a).\;...=(\sqrt2)^{3+4-5}=\sqrt2^2=2\\ b).\;...=(\frac{3}{4})^{12-7-4+1}=(\frac{3}{4})^2=9/16\\ c).\;...=(2/3)^{4\cdot5+3\cdot4-5\cdot4}=(2/3)^{12}[/tex]