Tag: powers

Questions Related to powers

If $\displaystyle { 2 }^{ n }-{ 2 }^{ n-1 }=4$, then the value of $\displaystyle { n }^{ n }$ will be -

maths indices exponentiation index notation and products of prime factors powers

  1. 1

  2. $\displaystyle \frac { 3 }{ 2 } $

  3. 2

  4. 27

Show answer
Correct Option: D
Explanation:

$\displaystyle { 2 }^{ n }-{ 2 }^{ n-1 }=4$
$\displaystyle \therefore \quad { 2 }^{ n-1 }\left( 2-1 \right) =4$
$\displaystyle \therefore \quad { 2 }^{ n-1 }={ 2 }^{ 2 }$
$\displaystyle \therefore \quad n-1=2$
$\displaystyle \therefore \quad n=3$
$\displaystyle \therefore \quad { n }^{ n }={ 3 }^{ 3 }=27$

$\displaystyle \frac { { \left( 3.63 \right)  }^{ 2 }-{ \left( 2.37 \right)  }^{ 2 } }{ 3.63+2.37 } $ is simplified to -

maths indices exponentiation index notation and products of prime factors powers

  1. 6

  2. 1.36

  3. 2.26

  4. 1.26

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac { { \left( 3.63 \right)  }^{ 2 }-{ \left( 2.37 \right)  }^{ 2 } }{ 3.63+2.37 } $
$\displaystyle =\frac { \left( 3.63+2.37 \right) \left( 3.63-2.37 \right)  }{ 3.63+2.37 } $
$\displaystyle =3.63-2.37$
$\displaystyle =1.26$

Value of $\displaystyle\frac{2^{100}}{2}$ is

maths indices exponentiation index notation and products of prime factors powers

  1. $1$

  2. $\displaystyle 50^{100}$

  3. $\displaystyle 2^{50}$

  4. $\displaystyle 2^{99}$

Show answer
Correct Option: D
Explanation:

$\displaystyle 2^{100}\div 2^1=2^{100-1}=2^{99}$

Simplest form of the Expression $\displaystyle { \left( { x }^{ 6 }.{ y }^{ { -5 }/{ 4 } } \right)  }^{ { -4 }/{ 3 } }$ will be-

maths indices exponentiation index notation and products of prime factors powers

  1. $\displaystyle { x }^{ -24 }y$

  2. $\displaystyle { x }^{ -8 }{ y }^{ { 5 }/{ 3 } }$

  3. $\displaystyle { x }^{ 8 }{ y }^{ { -5 }/{ 3 } }$

  4. $\displaystyle { x }^{ -8 }{ y }^{ { -5 }/{ 3 } }$

Show answer
Correct Option: B
Explanation:

$\displaystyle { \left( { x }^{ 6 }.{ y }^{ { -5 }/{ 4 } } \right)  }^{ { -4 }/{ 3 } }$
$\displaystyle ={ x }^{ -6\times { 4 }/{ 3 } }{ y }^{ \dfrac { -5 }{ 4 } \times -\dfrac { 4 }{ 3 }  }$
$\displaystyle ={ x }^{ -8 }{ y }^{ { 5 }/{ 3 } }$