Question

Scrieti folosind o singura putere:
A)3 la puterea 100 :3 la puterea 4 :3 la puterea 6:3 la puterea 10 : la 3 la puterea 7.
B)13 la puterea 4:13:13
C) 8 la puterea 9x8 la puterea 8:8 la puterea 10:8 la puterea 3.
D)12 la puterea 5: 12 la puterea 3x12 la puterea 6:12 la puterea 5 : 12 la puterea 2.
Scrieti,folosin o singura putere (3la puterea 4)5 x 3 la puterea 5.
B)16 la puterea 4 x4 la puterea 5:2 la puterea 5.
Va rog ajutati-ma!!

Answer 1

Răspuns:

Explicație pas cu pas:

A)     3¹⁰⁰ : 3⁴ : 3⁶ : 3¹⁰ : 3⁷ = 3⁽¹⁰⁰⁻⁴⁻⁶⁻¹⁰⁻⁷⁾ = 3⁷³

B)   13⁴ : 13¹ : 13¹ = 13⁽⁴⁻¹⁻¹⁾ = 13² = 169

C)   8⁹ x 8⁸ : 8¹⁰ : 8³ = 8⁽⁹⁺⁸⁻¹⁰⁻³⁾ = 8⁽¹⁷⁻¹³⁾ = 8⁴

D)   12⁵ : 12³ x 12⁶ : 12⁵ : 12² = 12⁽⁵⁻³⁺⁶⁻⁵⁻²⁾ = 12¹ = 12

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(3⁴)⁵ x 3⁵ = 3⁴ˣ⁵ x 3⁵ = 3²⁰⁺⁵ = 3²⁵

B)   16⁴ x 4⁵ : 2⁵ = (2⁴)⁴ x ( 2²)⁵ : 2⁵ = 2⁽¹⁶⁺¹⁰⁻⁵⁾ = 2²¹

Answer 2

Răspuns:

Explicație pas cu pas:

$a) \: {3}^{100} \div {3}^{4} \div {3}^{6} \div {3}^{10} \div {3}^{7} = \\ = {3}^{100 - 4 - 6 - 10 - 7} \\ = {3}^{96 - 6 - 10 - 7} \\ = {3}^{90 - 10 - 7} \\ = {3}^{8 0 - 7} \\ = \boxed{ {3}^{73} }$

$b) \: {13}^{4} \div 13 \div 13 \\ = {13}^{4} \div {13}^{1} \div {13}^{1} \\ = {13}^{4 - 1 - 1} \\ = {13}^{3 - 1} \\ = \boxed{ {13}^{2}}$

$c) \: {8}^{9} \times {8}^{8} \div {8}^{10} \div {8}^{3} = \\ = {8}^{9 + 8 - 10 - 3} \\ = {8}^{17 - 10 - 3} \\ = {8}^{7 - 3} \\ = \boxed{ {8}^{4} }$

$d) \: {12}^{5} \div {12}^{3} \times {12}^{6} \div {12}^{5} \div {12}^{2} = \\ = {12}^{5 - 3 + 6 - 5 - 2} \\ = {12}^{2 + 6 - 5 - 2} \\ = {12}^{8 - 5 - 2} \\ = {12}^{3 - 2} \\ = \boxed{ {12}^{1} }$

$a) \: ( {3}^{4} )^{5} \times {3}^{5} = \\ = {3}^{4 \times 5} \times {3}^{5} \\ = {3}^{20} \times {3}^{5} \\ = {3}^{20 + 5} \\ = \boxed{ {3}^{25} }$

$b) \: {16}^{4} \times {4}^{5} \div {2}^{5} = \\ = {( {2}^{4}) }^{4} \times {( {2}^{2} )}^{5} \div {2}^{5} \\ = {2}^{4 \times 4} \times {2}^{2 \times 5} \div {2}^{5} \\ = {2}^{16} \times {2}^{10} \div {2}^{5} \\ = {2}^{16 + 10 - 5} \\ = {2}^{26 - 5} \\ = \boxed{ {2}^{21} }$

Formule aplicate

${a}^{m} \times {a}^{n} = {a}^{m + n} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} \\ {( {a}^{m} )}^{n} = {a}^{m \times n}$