Tag: powers and exponents

Quizzes (12) Questions (35)

Questions Related to powers and exponents

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

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

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

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

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

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

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


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

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

$I=100$

  1. $F,G,H,I$
  2. $G,F,H,I$
  3. $F,H,G,I$
  4. $H,F,G,I$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $F>H>G>I$

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

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

  1. $-3.581$
  2. $-3.162$
  3. $-2.613$
  4. $-1.581$
  5. $-0.419$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $k<-1$)

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

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

  1. 2

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $0.00000004$