Question

Simplify and express the result in power notation with positive exponent:
(i) (-4)4 ÷(-4)8
(ii) (1/23)2
(iii) -(3)4×(5/3)4
(iv) (3-7÷3-10)×3-5
(v) 2-3×(-7)-3

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Answer 1

Hey Mate ! here are your solution!

1] (-4)⁴÷(-4)⁸

Remember the law which states that :

$\tt{ {x}^{a} \div {x}^{b} = {x}^{a - b} }$

Hence, (-4)⁴÷(-4)⁸

$\tt{ = { - 4}^{4 - 8} }$

$\tt{ = { - 4}^{ - 4} }$

$\tt{ = \frac{1}{ { - 4}^{4} } }$

Hence, This I your solution

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2] (1/2³)² (I think you have written this ?)

According to a law which state :

$\tt{( {x}^{a} {)}^{b} = {x}^{a \times b} }$

Hence, (1/2³)²

$\large\tt{ = (\frac{1}{ {2}^{3} } {)}^{2} }$

$\large \tt{ = \frac{ {1}^{2} }{ {2}^{2 \times 3} } }$

$\large\tt{ = \frac{1}{ {2}^{6} } }$

Hence, This is your solution.

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3] (-3)⁴×(5/3)⁴

According to a law,

$\tt{ {x}^{a} \times {y}^{a} = {(x \times y})^{a} }$

Hence, (-3)⁴×(5/3)⁴

$\large \tt{ = {( - 3 \times \frac{5}{3}) }^{4} }$

$\large \tt{ = {( - 5)}^{4} }$

Hence, This is your solution

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4]

$\tt{ ( {3}^{ - 7} \div {3}^{ - 10} ) \times {3}^{ - 5}}$

$\tt{ = ( {3}^{ - 7 + 10} ) \times {3}^{ - 5} }$

$\tt{ = {3}^{ - 3} \times {3}^{ - 5} }$

$\tt{ = {3}^{ 3 - 5} }$

$\tt{ = {3}^{ - 2} }$

$\large \tt{ = \frac{1}{ {3}^{2} } }$

Hence, This is your solution

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5]

$\tt{ {2}^{ - 3} \times { - 7}^{ - 3} }$

$\tt{ = {( - 7 \times 2)}^{ - 3} }$

$\tt{ = {( - 14)}^{ - 3} }$

$\large \tt{ = \frac{1}{ - 1 {4}^{3} }}$

Hence your solution are :

$\large \tt{1. \frac{1}{ { - 4}^{4} } }$

$\large \tt{2. \frac{1}{ {2}^{6} } }$

$\large \tt{3. {( - 5)}^{4} }$

$\large \tt{4. \frac{1}{ {3}^{2} } }$

$\large \tt{5. \frac{1}{ { - 14}^{3} }}$