Tag: laws of indices

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Questions Related to laws of indices

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

$5^{-2}$ can also be expressed as

  1. $\dfrac{1}{25}$
  2. $\dfrac{1}{5^{-2}}$
  3. $\dfrac{1}{5}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$5^{-2}=5^{-1*2}$

$=(5^2)^{-1}$                       $\because  (a)^{mn}=(a^m)^n$

$=\dfrac{1}{5^2}$                              $\because a^{-n}=\dfrac{1}{a^n}$

$=\dfrac{1}{25}$
Multiple choice maths indices negative indices law of indices laws of indices

If the exponent of a negative integer is odd, then the result is a .......... integer.

  1. positive

  2. negative

  3. zero

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

  If the exponent of a negative integer is odd, then the result is a negative integer.

$\Rightarrow$  $(-2)^{3}=(-2)\times (-2)\times (-2)=-8$
$\Rightarrow$  Here, $-2$ is negative base and $3$ is odd power.
$\Rightarrow$  Then result  $-8$ is a negative integer.

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