Tag: powers and exponents

Questions Related to powers and exponents

If $2^{3x - 2} = 16$, then calculate the value of $x $.

maths powers and exponents scientific notation use of exponents power of 10

  1. $\dfrac {1}{2}$

  2. $1$

  3. $2$

  4. $\dfrac {3}{2}$

Show answer
Correct Option: C
Explanation:

Given, ${ 2 }^{ 3x-2 }=16$
$\Rightarrow { 2 }^{ 3x-2 }=16={ 2 }^{ 4 }$

As bases are equal, there powers must be equal.
$\therefore 3x-2=4$
$\therefore 3x=6$
$\therefore x=2$

Place the following list of numbers with the given labels in order of greatest to least.
$F={({10}^{10})}^{10}$


$G={10}^{10}$ ${10}^{10}$

$H=\cfrac{{10}^{100}}{{10}^{10}}$

$I=100$

maths powers and exponents scientific notation use of exponents power of 10

  1. $F,G,H,I$

  2. $G,F,H,I$

  3. $F,H,G,I$

  4. $H,F,G,I$

Show answer
Correct Option: C
Explanation:

$F={({10}^{10})}^{10}=10^{10\times 10}=10^{100}$


$G={10}^{10}$ ${10}^{10}=10^{10+10}=10^{20}$

$H=\cfrac{{10}^{100}}{{10}^{10}}=10^{100-10}=10^{90}$

$I=100$

Clearly $F>H>G>I$

If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k < -1$, find the value of $k$.

maths powers and exponents scientific notation use of exponents power of 10

  1. $-3.581$

  2. $-3.162$

  3. $-2.613$

  4. $-1.581$

  5. $-0.419$

Show answer
Correct Option: A
Explanation:

Given, ${ 5 }^{ { k }^{ 2 } }({ 25 }^{ 2k })(625)=25\sqrt { 5 } $
${ 5 }^{ { k }^{ 2 }+4k+4 }={ 5 }^{ \tfrac 52 }$ 

By comparing powers, we get
${ k }^{ 2 }+4k+4=\cfrac 52$ which implies ${ 2k }^{ 2 }+8k+3=0$
$\Rightarrow k = -3.581$           ...(given $k<-1$)

$10^8$ is expanded by writing ............ number of zeros after 1

maths powers and exponents decimal fracfions measurements again understanding tenths and hundredths

  1. 8

  2. 0

  3. 10

  4. None of these

Show answer
Correct Option: A
Explanation:

8 zeros after 1 for $10^8$

A decimal number has 16 decimal places The number of decimal places in the square root of this number will be

maths powers and exponents decimal fracfions measurements again understanding tenths and hundredths

  1. 2

  2. 4

  3. 8

  4. 16

Show answer
Correct Option: C
Explanation:

The square root will have half the number of decimal places as the number it self has.
Hence square root of $16$ decimal places has $8$ decimal places.

For e.g. the square root of $0.0000000000000016$ will be $0.00000004$