Question

me pueden ayudar con eso porfa

Answer 1

Respuesta:

1)6

2)3

3)64

4)4

5)27

6)X²

7)81

8)16

Explicación paso a paso:

1)

$3 {x}^{a + 4} {y}^{b + 3} {z}^{c + 2} = - 2 {x}^{b + 4} {y}^{c + 3} {z}^{8}$

entonces:

${z}^{c + 2} = {z}^{8}$

c+2=8

c=6

${y}^{b + 3} = {y}^{c + 3}$

b+3=c+3

b=6+3-3

b=6

${x}^{a + 4} = {x}^{b + 4}$

a+4=b+4

a=6+4-4

a=6

$\frac{a + b + c}{3} = \frac{6 + 6 + 6}{3} = \frac{18}{3} = 6$

2)

$(2a + b) {x}^{4} {y}^{b + 3} = (b - 3a) {x}^{4a} {y}^{5}$

entonces:

${x}^{4} = {x}^{4a}$

4=4a

a=1

${y}^{b + 3} = {y}^{5}$

b+3=5

b=2

$(2a + b) + (b - 3a) =$

(2(1)+2)+(2-3(1))=(4)+(-1)=4-1=3

3)

${4}^{ {3}^{ {2}^{0} } } = {4}^{ {3}^{1} } = {4}^{3} = 64$

4)

$( {4}^{11} \div ( {4}^{7} \div {4}^{5} ) {)}^{3} \div {4}^{26}$

$( {4}^{11} \div ( {4}^{2} ) {)}^{3}$

$( {4}^{9} {)}^{3} \div {4}^{26}$

${4}^{27} \div {4}^{26} = 4$

5)

$( {3}^{6} \div ( {3}^{4} \div {3}^{1} )) \div ( {3}^{2} \div {3}^{5} {)}^{0}$

$( {3}^{6} \div {3}^{3} ) \div 1$

${3}^{3} \div 1 = 27 \div 1 = 27$

6)

$( \sqrt[3]{ \sqrt{ \sqrt[5]{ {x}^{0.5} } } } {)}^{120}$

$( \sqrt[3]{ \sqrt{ {x}^{ \frac{1}{10} } } } {)}^{120}$

$( \sqrt[3]{ {x}^{ \frac{1}{20} } } {)}^{120}$

$( {x}^{ \frac{1}{60} } {)}^{120}$

${x}^{2}$

7)

${3}^{ {2}^{ {2}^{ {7}^{ {0}^{ {5}^{2} } } } } } = {3}^{ {2}^{ {2}^{1} } } = {3}^{4} = 81$

8)

${256}^{ {2}^{ { - 7}^{ {0}^{7} } } } = {256}^{ {2}^{ - {7}^{0} } } = {256}^{ {2}^{ - 1} } = {256}^{ \frac{1}{ {2}^{1} } } = {256}^{ \frac{1}{2} } = \sqrt{256} = 16$