Question

Rezolvati exercitiile:
$(( - 5 ) ^{12} \times (5 ^2) ^5) ^3 \div ( - 5) ^{49}$
$( {3}^{4 } \times ( - 9) ^{4})^{2} \div {27}^{7}$
$(( { - 2})^{5} \times {3}^{5} )^{2} \div ( - 6) ^{9}$
$( - 4 ^{3} \times {2}^{5} )^{6} \div ( - 2)^{10}$
$( { - 7}^{3} ) ^{11} \div (( - 49) ^{8} \times {343}^{5} )$
$( - 5)^{83} \div (( - 5)^{22} \times {25}^{30}$
$( { - 3}^{3}) ^{40} \div (( - 3)^{27} \times {27}^{30}$
$( - 3)^{32} \div ( - 3) ^{30} + ( - 3) ^{32} \div ( - 3) ^{31}$
dau coroana+50 de puncte


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Answer 1

Răspuns: Ai rezolvarea mai jos

Explicație pas cu pas:

$\large \bf a)~~ \Big(( - 5 )^{12} \cdot (5^{2})^{5}\Big)^{3} : ( - 5)^{49}=$

$\large \bf \Big(5^{12} \cdot 5^{2\cdot5}\Big)^{3} : ( - 5)^{49}=\Big(5^{12} \cdot 5^{10}\Big)^{3} : ( - 5)^{49} =$

$\large \bf \Big(5^{12+10}\Big)^{3} : ( - 5)^{49}= \Big(5^{22}\Big)^{3} : ( - 5)^{49}=$

$\large \bf 5^{22\cdot3} : ( - 5)^{49}=5^{66} : ( - 5)^{49}=(-5)^{66-49}=$

$\color{blue}\Large \boxed{\bf (-5)^{17}}$

$\it~~$

$\large \bf b)~~\Big( {3}^{4 } \cdot (-9)^{4}\Big)^{2} : 27^{7}=$

$\large \bf \Big( {3}^{4 } \cdot 9^{4}\Big)^{2} : \Big(3^{3}\Big)^{7}= \Big( {3}^{4 } \cdot 3^{2\cdot4}\Big)^{2} : 3^{3\cdot7}=$

$\large \bf \Big( {3}^{4 } \cdot 3^{8}\Big)^{2} : 3^{21}=\Big( {3}^{4 +8}\Big)^{2} : 3^{21}=$

$\large \bf {3}^{12\cdot2} : 3^{21}={3}^{24} : 3^{21}={3}^{24-21}=$

$\color{blueviolet}\Large \boxed{\bf {3}^{3}}$

$\large\bf c)~~\Big(( {-2})^{5} \cdot {3}^{5}\Big)^{2} : (-6)^{9}=$

$\large\bf \Big((-6)^{5} \Big)^{2} : (-6)^{9}=(-6)^{5\cdot 2} : (-6)^{9}$

$\large\bf (-6)^{10} : (-6)^{9} = (-6)^{10-9} =(-6)^{1}=$

$\color{violet}\Large\boxed{\bf -6}$

$\it~~$

$\large \bf d)~~\Big(-4^{3} \cdot {2}^{5}\Big)^{6} : \big(-2\big)^{10}=$

$\large \bf \big(-(2^{2})^{3} \cdot {2}^{5}\big)^{6} : 2^{10}= \big(-2^{6} \cdot {2}^{5}\big)^{6} : 2^{10}=$

$\large \bf \big(-2^{11}\big)^{6} : 2^{10}=2^{11\cdot6} : 2^{10}=2^{66-10}=$

$\color{Magenta}\Large\boxed{ \bf 2^{56}}$

$\it~~~$

e) (-7³)¹¹ : [(-49)⁸ · 343⁵] =

(-7³ˣ¹¹) : [(-7²)⁸ · (7³)⁵] =

(-7³³) : (7¹⁶ · 7¹⁵) =

(-7³³) : 7³¹ =

-7³

=====================

f) (-5)⁸³ : [(-5)²² · 25³⁰] =

(-5)⁸³ : [(-5)²² · (5²)³⁰] =

(-5)⁸³ : [(-5)²² · 5⁶⁰] =

(-5)⁸³ : (-5)⁸² =

5⁸³⁻⁸² =

5¹ =

5

=====================

g) (-3³)⁴⁰ : [(-3)²⁷ · 27³⁰] =  

3¹²⁰ : [(-3)²⁷ · (3³)³⁰] =

3¹²⁰ : [(-3)²⁷ · 3⁹⁰] =

3¹²⁰ : (-3)¹¹⁷ =

- 3³

=====================

h) (-3)³² : (-3)³⁰ + (-3)³² : (-3)³¹ =

(-3)³²⁻³⁰ + (-3)³²⁻³¹ =

(-3)² + (-3)¹ =

9 - 3 =

6

==pav38==