Tag: powers and exponents

Questions Related to powers and exponents

Write the number of significant digits in:
$0.97 \times 10^{-2}$

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

  1. $1$

  2. $5$

  3. $2$

  4. $3$

Show answer
Correct Option: C
Explanation:

$0.97\times 10^{-2}$
There are $2$ significant figures $9$ and $7$. When a number is  written in scientific notation, only significant figures are placed into the numerical portion.

$225$ can be expressed as

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

  1. $5\times 3^2$

  2. $5^2\times 3$

  3. $5^2\times 3^2$

  4. $5^3\times 3$

Show answer
Correct Option: C
Explanation:

$ 225 = 25 \times 9$
$ 225 = (5\times 5)  \times (3 \times 3)$

$ 225 = 5^2 \times 3^2$
Option C is correct

Which of the following is greater than 1000.01 ?

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

  1. 0.00010001 x 10$\displaystyle ^{7}$

  2. 0.00001 x 10$\displaystyle ^{8}$

  3. 1.1 x 10$\displaystyle ^{2}$

  4. 1.00001 x 10$\displaystyle ^{3}$

Show answer
Correct Option: A
Explanation:

A $\Rightarrow \displaystyle 0.00010001\times 10^{7}=1000.1 $
B $\Rightarrow \displaystyle 0.00001\times 10^{8}=1000 $
C $\Rightarrow \displaystyle 1.1\times 10^{2}=110 $
D $\Rightarrow \displaystyle 1.00001\times 10^{3}=1000.01 $

We observe that $\displaystyle 1000.1> 1000.01 $
i.e., $\displaystyle 0.00010001\times 10^{7}> 1000.01 $

What is the smallest integer n for which $\displaystyle { 25 }^{ n }>{ 5 }^{ 12 }$?

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

  1. $6$

  2. $7$

  3. $8$

  4. $9$

  5. 10

Show answer
Correct Option: B
Explanation:

${25}^{n}>{5}^{12}$

${({5}^{2})}^{n}>{5}^{12}$
${{5}^{2n}}>{5}^{12}$
Comparing the power
$2n>12$
$n>\dfrac{12}{2}$
$n>6$
Smallest integer greater than $6$ will be $7$

If $4^{n-2} + 4^{2} = 32$, then what is the value of $n$?

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

  1. $2$

  2. $4$

  3. $6$

  4. $8$

Show answer
Correct Option: B
Explanation:

Given, ${ 4 }^{ n-2 }+{ 4 }^{ 2 }=32$
${ 4 }^{ n-2 }=32-{ 4 }^{ 2 }$
${ 4 }^{ n-2 }=32-16$
${ 4 }^{ n-2 }=16$
${ 4 }^{ n-2 }={ 4 }^{ 2 }$
$n-2=2$ ..... (as the bases are equal)
$n=4$

If $\sqrt { { 2 }^{ x } } =16$, then $x=$

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

  1. $8$

  2. $4$

  3. $2$

  4. $10$

Show answer
Correct Option: A
Explanation:

$\sqrt { { 2 }^{ x } } =16\ \Rightarrow { (2) }^{ \dfrac { x }{ 2 }  }={ 2 }^{ 4 }$


Exponents should be equal.

$ \dfrac { x }{ 2 } =4\Rightarrow x=8$

If $2^x - {2^{x - 1}} = 4$ then $x^x$ is equals to 

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

  1. $7$

  2. $3$

  3. $27$

  4. None of these

Show answer
Correct Option: C
Explanation:
$2^{x}-2^{x-1}=4$

$2^{x}-2^{x}2^{-1}=4$

$2^{x}\left (1-\dfrac{1}{2}\right )=2^{x-1}=4=2^2$

$\therefore$ $x-1=2$

$\text{from this we get }$  $x=3$

$x^{x}=3^{3}=27$

If $3^x=5^y=7^z=105$, then $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}$ is equal to?

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

  1. $1$

  2. $0$

  3. $-1$

  4. None

Show answer
Correct Option: A
Explanation:

$x = \cfrac{\log 105}{\log 3}, y = \cfrac{\log 105}{\log 5} , z = \cfrac{\log 105}{\log 7}$

$\cfrac{1}{x} + \cfrac{1}{y} + \cfrac{1}{z} = \cfrac{\log 3 + \log 5 + \log 7}{\log 105} = \cfrac{\log 105}{\log 105} = 1$

Which is greatest among following $2^{156},\ 4^{79},\ 128^{23}$ and $8^{54}$?

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

  1. $4^{79}$

  2. $128^{23}$

  3. $2^{156}$

  4. $8^{54}$

Show answer
Correct Option: D
Explanation:
$2^{156}\rightarrow 2^{156}$
$4^{79}\rightarrow {2^{2\times 79}}\rightarrow 2^{158}$
$128^{23}\rightarrow 2^{7\times 23}\rightarrow 2^{161}$
$8^{54}\rightarrow 2^{3\times 54}\rightarrow 2^{162}$
$8^{54}$ is greatest
D is correct.

If $ { 9 }^{ x-1 }={ 3 }^{ 2x-1 }-486 $,then the value of x is:

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

  1. $\dfrac{7}{2}$

  2. 4

  3. 1

  4. 0

Show answer
Correct Option: A
Explanation:
$9^{x-1}=3^{2x-1}-486$
$3^{2x-1}=9^{x-1}t486$
$\dfrac{3^{2x}}{3}=3^{2x-2}+486$
$3^{2x}=\dfrac{3(3^{2x})}{3^{z}}t(486)3$
$3^{2q}=3^{2x-1}+1458$
$2177=729+1458$
$3^{7}=3^{6}+1458$
$2x=7$
$x=\dfrac{7}{2}$