Exponents and Powers Test

Result

Exponents and Powers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following has a negative index?

A
$$ \dfrac { 1 }{ { x }^{ -3 } } $$

B
$${ x }^{ 3 }$$

C
$${ -x }^{ 3 }$$

D
$$\dfrac { 1 }{ { x }^{ 3 } } $$

Solution

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

Hence, option $$D$$ is correct.
Question 2
1 / -0

Which of the following has a negative index?

A
$${ x }^{ 5 }$$

B
$$\dfrac { 1 }{ x } $$

C
$${ (x) }^{ \tfrac { 3 }{ 2 } }$$

D
$${ (-x) }^{ \tfrac { 3 }{ 2 } }$$

Solution

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

Hence, option $$B$$ is correct
Question 3
1 / -0

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

A
$$\dfrac {3}{8}$$

B
$$\dfrac {-3}{8}$$

C
$$\dfrac {8}{3}$$

D
$$\dfrac {-8}{3}$$

Solution

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 $$\left (\dfrac {4}{3} - 4\right)^{-1}$$ $$=$$ $$\left (\dfrac {-8}{3}\right)^{-1}$$ $$=$$ $$-\dfrac {3}{8}$$
Question 4
1 / -0

Which of the following has a negative index?

A
$$\dfrac { 1 }{ { x }^{ 2 } } $$

B
$${ (x) }^{ \tfrac { 1 }{ 4 } }$$

C
$${ (-x) }^{ 2 }$$

D
$$\dfrac { 1 }{ { x }^{ -2 } } $$

Solution

$$\dfrac { 1 }{ { x }^{ 2 } } $$ = $${ x }^{ -2 }$$
Thus $${ x }^{ -2 }$$ has a negative index
Therefore option $$A$$ is the correct answer.
Question 5
1 / -0

Which of the following has a negative index?

A
$${ (x) }^{ \tfrac{ 1 }{4 } }$$

B
$${ (x) }^{ \tfrac { 2 }{ 3 } }$$

C
$$\dfrac { 1 }{ { x }^{ 2 } } $$

D
$${ (-x) }^{\tfrac { 2 }{ 3 } }$$

Solution

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
Question 6
1 / -0

Simplify:
$$\left(\dfrac{27}{125}\right)^{-1}=$$

A
$$\dfrac{3}{5}$$

B
$$\left(\dfrac{3}{5}\right)^{-1}$$

C
$$\left(\dfrac{3}{5}\right)^{-2}$$

D
$$\left(\dfrac{5}{3}\right)^{3}$$

Solution

$${\left(\dfrac{125}{27}\right)}^{1}$$ using $$\dfrac{1}{{a}^{m}}={a}^{-m}$$
$$=\dfrac{{5}^{3}}{{3}^{3}}$$
$$={\left(\dfrac{5}{3}\right)}^{3}$$
Question 7
1 / -0

Choose the correct answer from the given four options:
$$\bigg(-\dfrac{3}{2}\bigg)^{-1}$$ is equal

A
$$\dfrac{2}{3}$$

B
$$-\dfrac{2}{3}$$

C
$$\dfrac{3}{2}$$

D
$$\dfrac{4}{9}$$

Solution

$$\bigg(-\dfrac{3}{2}\bigg)^{-1} =-\dfrac{2}{3}$$
Question 8
1 / -0

Fill in the blanks:
$$0.000008$$ _______ $$0.000016$$

A
is half of

B
is double of

C
is one-fourth of

D
is one-third of
Question 9
1 / -0

Difference of the greatest $$7$$ digit number and the smallest $$ 5$$ digit number is

A
$$9,98,999$$

B
$$99,89,999$$

C
$$99,899$$

D
$$9,98,099$$

Solution

$$\textbf{Step-1: Find greatest 7 digit number and smallest 5 digit number}$$
$$\text{We know greatest n digit number is= 9999..n times }$$
$$\text{And smallest n digit number is= 10000..(n-1) times }$$
$$\text{ So 7- digit greatest number}$$$$=99,99,999$$
$$\text{And 5-digit smallest number}$$ $$=10,000$$

$$\textbf{Step-2: Find Difference}$$
$$\text{Difference}$$ $$=99,99,999-10,000=99,89,999$$

$$\textbf{Hence Option B is correct.}$$
Question 10
1 / -0

Fill in blank with an appropriate comparison symbol.
$$0.00000998$$ ______ $$0.0000116$$

A
$$<$$

B
$$>$$

C
$$=$$

D
None of these

Solution

$$\displaystyle 0\cdot 00000998= 9\cdot 89\times 10^{-6}$$
$$\displaystyle 0\cdot 0000116= 1\cdot 16\times 10^{-5}$$
Thus $$\displaystyle 9\cdot 89\times 10^{-6}< 1\cdot 16\times 10^{-5}$$

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 16

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Exponents and Powers Test - 16

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SHARING IS CARING

Question 1

$$ \dfrac { 1 }{ { x }^{ -3 } } $$

$${ x }^{ 3 }$$

$${ -x }^{ 3 }$$

$$\dfrac { 1 }{ { x }^{ 3 } } $$

Solution

Question 2

$${ x }^{ 5 }$$

$$\dfrac { 1 }{ x } $$

$${ (x) }^{ \tfrac { 3 }{ 2 } }$$

$${ (-x) }^{ \tfrac { 3 }{ 2 } }$$

Solution

Question 3

$$\dfrac {3}{8}$$

$$\dfrac {-3}{8}$$

$$\dfrac {8}{3}$$

$$\dfrac {-8}{3}$$

Solution

Question 4

$$\dfrac { 1 }{ { x }^{ 2 } } $$

$${ (x) }^{ \tfrac { 1 }{ 4 } }$$

$${ (-x) }^{ 2 }$$

$$\dfrac { 1 }{ { x }^{ -2 } } $$

Solution

Question 5

$${ (x) }^{ \tfrac{ 1 }{4 } }$$

$${ (x) }^{ \tfrac { 2 }{ 3 } }$$

$$\dfrac { 1 }{ { x }^{ 2 } } $$

$${ (-x) }^{\tfrac { 2 }{ 3 } }$$

Solution

Question 6

$$\dfrac{3}{5}$$

$$\left(\dfrac{3}{5}\right)^{-1}$$

$$\left(\dfrac{3}{5}\right)^{-2}$$

$$\left(\dfrac{5}{3}\right)^{3}$$

Solution

Question 7

$$\dfrac{2}{3}$$

$$-\dfrac{2}{3}$$

$$\dfrac{3}{2}$$

$$\dfrac{4}{9}$$

Solution

Question 8

is half of

is double of

is one-fourth of

is one-third of

Question 9

$$9,98,999$$

$$99,89,999$$

$$99,899$$

$$9,98,099$$

Solution

Question 10

$$<$$

$$>$$

$$=$$

None of these

Solution

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