Tag: maths

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Multiple choice maths indices negative indices law of indices laws of indices

If the exponent of a negative integer is even then the result is a ............ integer.

  1. Positive

  2. Negative

  3. 0

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

  If the exponent of a negative integer is even, then the result is a $positive$ integer.

$\Rightarrow$  $(-2)^{4}=(-2)\times (-2)\times (-2)\times(-2)=16$
$\Rightarrow$  Here, $-2$ is negative base and $4$ is even power.
$\Rightarrow$  Then result  $16$ is a positive integer.

Multiple choice maths indices negative indices law of indices laws of indices

Evaluate : $(-4)^{-2}$---

  1. $\displaystyle \frac{1}{-16}$
  2. $\displaystyle \frac{1}{16}$
  3. $-16$
  4. $16$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$(-4)^{-2}=\dfrac{1}{(-4)^2}$            $\because a^{-m}=\dfrac{1}{a^m}$

$=\dfrac{1}{-4*-4}$

$=\dfrac1{16}$

$\therefore(-4)^{-2}=\dfrac1{16}$
Multiple choice maths indices negative indices law of indices laws of indices

Which of the following has an exponent with negative index?

  1. $-3^{4}$
  2. $4^{3}$
  3. $\dfrac {1}{3^{4}}$
  4. $-3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

$\therefore \dfrac {1}{3^{4}}$ has a negative index.
So, option $C$ is correct.

Multiple choice maths indices negative indices law of indices laws of indices

Which of the following has a negative index?

  1. ${ x }^{ 5 }$
  2. $\dfrac { 1 }{ x } $
  3. ${ (x) }^{ \tfrac { 3 }{ 2 } }$
  4. ${ (-x) }^{ \tfrac { 3 }{ 2 } }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{1}{x} = x^{-1}$. Index of $x$ is $(-1)$, which is negative.


Hence, option $B$ is correct

Multiple choice maths indices negative indices law of indices laws of indices

Which of the following has a negative index?

  1. $ \dfrac { 1 }{ { x }^{ -3 } } $
  2. ${ x }^{ 3 }$
  3. ${ -x }^{ 3 }$
  4. $\dfrac { 1 }{ { x }^{ 3 } } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac{1}{x^3}=x^{-3}$ . Index of $x$ is  $(-3)$, which is negative.


Hence, option $D$ is correct.

Multiple choice maths indices negative indices law of indices laws of indices

Which of the following has a negative index?

  1. $\dfrac { 1 }{ { x }^{ 2 } } $
  2. ${ (x) }^{ \tfrac { 1 }{ 4 } }$
  3. ${ (-x) }^{ 2 }$
  4. $\dfrac { 1 }{ { x }^{ -2 } } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac { 1 }{ { x }^{ 2 } } $ = ${ x }^{ -2 }$
Thus ${ x }^{ -2 }$ has a negative index
Therefore option $A$ is the correct answer.

Multiple choice maths indices negative indices law of indices laws of indices

Which of the following has a negative index?

  1. ${ (x) }^{ \tfrac{ 1 }{4 } }$
  2. ${ (x) }^{ \tfrac { 2 }{ 3 } }$
  3. $\dfrac { 1 }{ { x }^{ 2 } } $
  4. ${ (-x) }^{\tfrac { 2 }{ 3 } }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Option A has positive index i.e. $\dfrac {1}{4}$.
Option B also has positive index i.e., $\dfrac {2}{3}$
In option C, $\dfrac{1}{x^2} = x^{-2}$.  
Index of $x$ is $(-2)$, which is negative.
Hence, option C is correct

Multiple choice maths indices negative indices law of indices laws of indices

If $\dfrac {p}{q} = \left (\dfrac {2}{3}\right )^{3} \div \left (\dfrac {3}{2}\right )^{-3}$, then the value of $\left (\dfrac {p}{q}\right )^{10}$ is _______.

  1. $1$
  2. $0$
  3. $-1$

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $\dfrac {p}{q} = \left (\dfrac {2}{3}\right )^{3} \div \left (\dfrac {3}{2}\right )^{-3}$
We see that, $\left (\dfrac{3}{2}\right )^{-3}$=$\left (\dfrac{2}{3}\right)^{3}$
So, $\left (\dfrac{2}{3}\right)^{3}$ / $\left (\dfrac{2}{3}\right)^{3}$ $= 1$ 
Thus, $\left(\dfrac {p}{q}\right)^{10}=1$
Hence, A is the right answer.
Multiple choice maths indices negative indices law of indices laws of indices

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

  1. $\dfrac {3}{8}$
  2. $\dfrac {-3}{8}$
  3. $\dfrac {8}{3}$
  4. $\dfrac {-8}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need to find value of $\left { \left (\dfrac {3}{4}\right )^{-1} - \left (\dfrac {1}{4}\right )^{-1}\right }^{-1} $
It can be written as $\left (\dfrac {4}{3} - 4\right)^{-1}$ $=$ $\left (\dfrac {-8}{3}\right)^{-1}$ $=$ $-\dfrac {3}{8}$