Question

Por favor.... Podem me ajudar com isso??

Answer 1

Resposta:

1. a) $7.10^9$

  b) $2,078.10^{-6}$

  c) $10.10^{-4}$ =

  d) $4,9.10^2$

  e) $3,5.10^{-8}$

2. a) $10.10^{-6}$

   b) $2,19.10^6$

   c) $5.10^5$

   d) $10.10^{10}$

   e) $5.10^{-62}$

   f) $4,46.10^8$

   g) $-10.10^7$

   h) $8,1.10^{-6}$

   i) $2.10^0$

   j) $2.10^2$

   k) $7.10^{10}$

Explicação passo-a-passo:

2. a) $10^{-19}.10^3=10^{-19+3}=10^{-16}=10.10^{-16}$

   b) $7,3.10^{2}.3.10^4=7,3.3.10^2.10^4=21,9.10^6=2,19.10^6$

   c) $15.10^{-3}:3.10^8=15:3.10^{-3}.10^8=5.10^{-3+8}=5.10^5$

   d) $10^1:10^{-9}=10^{1-(-9)}=10^{1+9}=10^{10}=10.10^{10}$

   e) $410.10^{-31}+90.10^{-31}=410+90.10^{-31}.10^{-31}=500.10^{-31+(-31)}=5.10^{-31-31}=5.10^{-62}$

   f) $4,5.10^3-0,04.10^5=4,5-0,04.10^3.10^5=4,46.10^{3+5}=4,46.10^8$

   g) $5.10^4-6.10^2=5-6.10^4.10^2=-1.10^{4+2}=-1.10^6=-10.10^6=-10^{1+6}=-(10^7)=-10.10^7$

   h) $(9.10^{-3})^2=9^2.(10^{-3})^2=81.10^{(-3).2}=8,1.10^{-6}$

   i) $5.10^2+(2.10^{-1})^2=5.10^2+2^2.(10^{-1})^2=5.10^2.4.10^{(-1).2}=5.10^2.4.10^{-2}=5.4.10^2.10^{-2}=20.10^{2+(-2)}=2.10^{2-2}=2.10^0$

   j) $\sqrt[3]{8.10^6} =\sqrt[3]{8}.\sqrt[3]{10^6}=2.\sqrt[3]{1000000}=2.100=2.10^2$

   k) $\sqrt{49.10^{10}}=\sqrt{49}.\sqrt{10^{10}}=7.10000000000=7.10^{10}$

Answer 2

1 – a)

$7.000.000.000.0 = 7 \times {10}^{9}$

b)

$0.000002078 = 2.078 \times {10}^{ - 6}$

c)

$0.000100 = 1 \times {10}^{ - 4}$

d)

$490 = 4.90 \times {10}^{2}$

e)

$0.0000000350 = 3.50 \times {10}^{ - 8}$

2 – a)

${10}^{ - 19} \times {10}^{3} \\ = {10}^{ - 19 + 3} \\ = {10}^{ - 16} \\ = \frac{1}{ {10}^{16} }$

b)

$7.3 \times {10}^{2} \times 3 \times {10}^{4} \\ = 7.3 \times {10}^{2 + 4} \times 3 \\ = .3 \times {10}^{6} \times 3 \\ = 21900000$

c)

$15 \times {10}^{ - 3} \div 3 \times {10}^{4} \\ = 5 \div {10}^{ 7} \\ = 5 \div {2}^{7} \times {5}^{7} \\ = 1 \div {2}^{7} \times {5}^{6} \\ = \frac{1}{2000000}$

d)

${10}^{1} \div {10}^{ - 9} \\ = {10}^{1 - ( - 9)} \\ = {10}^{1 + 9} \\ = {10}^{10}$

e)

$410 \times {10}^{ - 31} + 90 \times {10}^{ - 31} \\ = \frac{41x}{ {2}^{30} \times {5}^{ = 30} } + \frac{9}{ {2}^{30} \times {5}^{30} } \\ = \frac{41x + 9}{ {2}^{30} \times {5}^{30} }$

f)

$4.5 \times {10}^{3} - 0.04 \times {10}^{5} \\ = 4500 - 4000 \\ = 500$

g)

$5 \times {10}^{4 } - 6 \times {10}^{2} \\ 5 \times 10^{4} = 50000 \\ 6 \times {10}^{2} = 600 \\ = 50000 - 600 \\ = 49400$

h)

$(9 \times {10}^{ - 3})^{2} \\ = {9}^{2} \times ( {10}^{ - 3})^{2} \\ = 81 \times ( {10}^{ - 3})^{2} \\ = 81 \times {10}^{ - 6} \\ = 81 \times \frac{1}{ {10}^{6} } \\ = 81 \times \frac{1}{1000000} \\ = \frac{81}{1000000}$

i)

$5 \times {10}^{2} + (2 \times {10}^{ - 1})^{2} \\ = {10}^{2} \times 5 \times \frac{1}{ {5}^{2} } \\ \frac{500 \times 25}{25} + \frac{1}{25} \\ = \frac{500 \times 25 + 1}{25} \\ = \frac{12501}{25}$

j)

$\sqrt[3]{8 \times {10}^{6} } \\ = \sqrt[3]{8} \sqrt[3]{ {10}^{6} } \\ = 2 \sqrt[3]{ {10| }^{6} } \\ = 2 \times 100 \\ = 200$

k)

$\sqrt{49 \times {10}^{10} } \\ = \sqrt{49} \sqrt{ {10}^{10} } \\ = 7 \sqrt{ {10}^{10} } \\ = 7 \times {10}^{5} \\ = 700000$