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

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

  1. $1$
  2. $5$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

Which of the following is greater than 1000.01 ?

  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$\displaystyle ^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $

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

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

  1. $6$
  2. $7$
  3. $8$
  4. $9$

  5. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $7$

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

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

  1. $1$
  2. $0$
  3. $-1$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

  1. $4^{79}$
  2. $128^{23}$
  3. $2^{156}$
  4. $8^{54}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
Multiple choice maths powers and exponents scientific notation use of exponents power of 10

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

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

  2. 4

  3. 1

  4. 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$9^{x-1}=3^{2x-1}-486$
$3^{2x-1}=9^{x-1}t486$
$\dfrac{3^{2x}}{3}=3^{2x-2}+486$
$3^{2x}=\dfrac{3(3^{2x})}{3^{z}}t(486)3$
$3^{2q}=3^{2x-1}+1458$
$2177=729+1458$
$3^{7}=3^{6}+1458$
$2x=7$
$x=\dfrac{7}{2}$