Question

Help me and answer this ..I will be much grateful to you....I will be definitely mark you the brainliest if your answer will be correct....help me please ...no spams....please

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Answer 1

$\huge\bold{Solutions:-}$

1)${3}^{ - 3} = \frac{1}{ {3}^{3} }$

So, multiplicative inverse of

${3}^{ - 3} \: \: is \: \: {3}^{3}$

Verification:-

${3}^{ - 3} \times {3}^{3} = 1$

$\frac{1}{ {3}^{3} } \times {3}^{3} = 1$

$\frac{1}{27} \times 27 = 1$

$1 = 1$

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2)We have,

${a}^{m} \times {a}^{n} = {a}^{m + n}$

$( - {5})^{2} \times ( - {5})^{ - 3}$

$( - 5)^{2 + ( - 3)}$

$= { (- 5)}^{ - 1}$

We have,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

So,

${( - 5)}^{ - 1} = - \frac{1}{ { 5}^{1} } = - \frac{1}{5}$

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3)Refer to the photo - 1

Answer is

$(\frac{2}{3} )^{5}$

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4)${(8)}^{ - 4} = (2 \times 4)^{ - 4}$

$= > (2 \times {2}^{2} ) ^{ - 4} = ({2}^{1 + 2} ) ^{ - 4}$

$( {2}^{3} )^{ - 4} = {2}^{3 \times - 4} = {2}^{ - 12}$

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5)$( \frac{ {3}^{6} }{ {3}^{8} } )^{4} \times ( {3})^{ - 4}$

We have ,

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$( {3}^{6 - 8} )^{ - 4}$

$( {3}^{ - 2} ) ^{4}$

We have,

$( {a}^{m} )^{n} = {a}^{mn}$

$( {3}^{ - 2} ) ^{4} = {3}^{ - 2 \times 4} = {3}^{ - 8}$

${3}^{ - 8} \times {3}^{ - 4}$

${3}^{ - 8 + ( - 4)} = {3}^{ - 12}$

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6)$( { - 2})^{k + 1} \times ( { - 2}^{3} ) = ( { - 2})^{7}$

${a}^{m} \times {a}^{n} = {a}^{m + n}$

$( { - 2})^{k + 1 + 3} = ( { - 2})^{7}$

Bases are equal. So,powers also equal

$k + 4 = 7$

$k = 7 - 4 = 3$

$k = 3$

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7)Refer to the photo-2

Final answer:-

$\frac{37}{16}$

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8)$(( { \frac{3}{4} })^{ - 2})^{2}$

We have,

$({a}^{m} )^{n} = {a}^{mn}$

$(\frac{3}{4} )^{ - 2 \times 2} = (\frac{3}{4}) ^{ - 4}$

We have,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

$(\frac{3}{4} )^{ - 4} = ( { \frac{4}{3} })^{4}$

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9)$0.0035 = \frac{35}{10000}$

$= > \frac{35}{ {10}^{4} } = 35 \times ({10})^{ - 4}$

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10)

Refer to the photo - 3

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Hope this is helpful $\huge\bold{✓}$