Tag: laws of exponents and powers

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Questions Related to laws of exponents and powers

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Simplify and give reasons:
${ \left( \cfrac { 1 }{ 2 }  \right)  }^{ -3 }\times { \left( \cfrac { 1 }{ 4 }  \right)  }^{ -3 }\times { \left( \cfrac { 1 }{ 5 }  \right)  }^{ -3 }\quad $

  1. ${40}^{3}$
  2. ${40}^{-3}$
  3. ${40}^{6}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

we know,

$(\dfrac{a}{b})^{-m}=(\dfrac{b}{a})^{m}$
So,
$(\dfrac{1}{2})^{-3}=(\dfrac{2}{1})^{3}=2^{3}$

$(\dfrac{4}{1})^{-3}=(\dfrac{4}{1})^{3}=4^{3}$

$(\dfrac{5}{1})^{-3}=(\dfrac{5}{1})^{3}=5^{3}$
now we know,

\$a^{m}b^{m}*c^{m}=(abc)^{m}$

$\implies(2)^{3}(4)^{3}*(5)^{3}$

$=(40)^{3}$

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Choose the correct option:
$\left[\dfrac{{100}}{{101}}\right]^3$

  1. $\dfrac{{100}^3}{{101}^3}$
  2. $\dfrac{{100}^4}{{101}^4}$
  3. $\dfrac{{1000}^2}{{101}^2}$
  4. $\dfrac{{100}}{{101}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \left[ \dfrac { 100 }{ 101 }  \right] ^{ 3 }\quad \ \quad \quad =\quad \dfrac { { 10 }0^{ 3 } }{ 101^{ 3 } } \quad \left( \because \left( \dfrac { { a }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a }{ b }  \right) ^{ m } \right) \ $

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Choose the correct options:$\dfrac{{10}^2}{{11}^2}$

  1. $\left[\dfrac{{10}}{{11}}\right]^2$
  2. $\left[\dfrac{{100}}{{11}}\right]^2$
  3. $\left[\dfrac{{10}}{{11}}\right]^4$
  4. $\left[\dfrac{{5}}{{11}}\right]^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \dfrac { { 10 }^{ 2 } }{ 11^{ 2 } } \ =\quad \left( \dfrac { 10 }{ 11 }  \right) ^{ 2 }\left( \because \left( \dfrac { { a }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a }{ b }  \right) ^{ m } \right) $

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Choose the correct option:
$\left(\dfrac{5^5\times6^5}{3^5}\right)$

  1. $\left(\dfrac{5\times6}{3}\right)^5$
  2. $\left(\dfrac{5\times6}{3}\right)^6$
  3. $\left(\dfrac{5\times6}{5}\right)^3$
  4. $\left(\dfrac{5\times6}{5}\right)^5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \left( \dfrac { { 5 }^{ 5 }\times { 6 }^{ 5 } }{ { 3 }^{ 5 } }  \right) \quad \ \quad \quad =\quad \left( \dfrac { 5\times 6 }{ 3 }  \right) ^{ 5 }\quad \left( \because \left( \dfrac { { a }^{ m }\times { c }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a\times c }{ b }  \right) ^{ m } \right) $