Question

Ajutorrrrr am nevoie de ajutor vă roggggggggggggg ​

Answer 1

$\huge \boxed{ \green{{a}^{x} \times {a}^{y} = {a}^{x + y} }}$

10)

a)

$\bf1,4 {}^{1} \times 1,4 {}^{2} \times 1,4 {}^{3} \times ... \times 1,4 {}^{99} = \\ = \bf 1,4 {}^{1 + 2 + 3 + .. + 99} = \\ = \bf 1,4 {}^{99 \times( 99 + 1) \div 2} = \\ \bf= 1,4 {}^{99 \times 100 \div 2} = \\ = \bf1,4 {}^{99 \times 50} = \\ \boxed{ \bf= 1,4 {}^{4950} }$

b)

$\bf2,5 {}^{2} \times 2,5 {}^{4} \times \bf2,5 {}^{6} \times ... \times 2.5 {}^{100} = \\ \bf= 2,5 {}^{2 + 4 + 6 + ... + 100} = \\ \bf = \bf 2,5 {}^{2(1 + 2 + 3 + ... + 50)} = \\ \bf = 2,5 {}^{2 \times 50 \times 51 \div 2} = \\ = \bf2,5 {}^{50 \times 51} = \\ \boxed{ \bf= 2,5 {}^{2550} }$

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Am folosit formula lui Gauss:

1+2+3+...+n = n•(n+1):2

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d)1,7^(2•3•5•7+1000)=

1,7^(210+1000)=

= 1,7^1210