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

Which of the following represents the given expression?
$a^2b^3\times 2ab^2$ ?

  1. $2a^3b^4$
  2. $2a^3b^5$
  3. $2ab$
  4. $a^3b^5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We know that if a number say $b$ is multiplied three times. That is, $b\times b\times b$ can be written as $b^3$.
=> $b^{3}$ = $b\times b\times b$
Similarly,
$a^{2}b^3$ = $a \times a\times b\times b\times b$
$2ab^{2}$ = $ 2 \times a\times b\times b$.
Thus, 
$a^{2}b^{3}\times 2ab^{2} = a \times a\times b\times b\times b \times 2 \times a\times b\times b $.
                      $= 2 \times a \times a \times a\times b\times b\times b\times b\times b$.
                      $ = 2a^{3}b^{5}$.
Multiple choice maths powers and exponents scientific notation use of exponents power of 10

If $\displaystyle 2^{2^{3}}=j, 2^{3^{2}}=k, 3^{2^{2}}=\varphi ,$ then 

  1. $k = 2j$
  2. $j < k$
  3. $\displaystyle \varphi < k$

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

  $j=2^{2{^3}}$, $k=2^{3^{2}}$, $\varphi=3^{2^{2}}$

$\Rightarrow$  $j=256,\,\,k=512,\,\,\varphi=81$
$\Rightarrow$  Option A says $k=2j$, which is true because $j=256$, so $k=2\times 256=512$
$\Rightarrow$  Option B says $j<k$, which is true because value of $j$ is $255$ and value of $k$ is $512$
$\Rightarrow$   Option C says $\varphi <k$, which is true because value of $\varphi$ is $81$ and value of $k$ is $512$

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

If $\displaystyle a^{m}=b^{m}$ and $(m > 0)$, then which of the following options could be true:

  1. $a = -b$
  2. $a + b= 0$
  3. $2a - b = 0$
  4. $\displaystyle \dfrac{a^{2}}{b^{2}}=1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $a^m=b^m$


Dividing by $b^m$

$\dfrac{a^m}{b^m}=1$
${\left(\dfrac{a}{b}\right)}^m=1$

Only Option D satisfies this answer.

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

Use an appropriate comparison symbol $0.00000998$ ______ $0.0000116$.

  1. $<$
  2. $>$
  3. $=$

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

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

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

$0.000008$ _______ $0.000016$

  1. is half of

  2. is double than

  3. is one-fourth of

  4. is one-third of
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle 0\cdot 000008= 8\times 10^{-6}$


$\displaystyle 0\cdot 000016= 1\cdot 6\times 10^{-5}$
Now
$\displaystyle \frac{8\times 10^{-6}}{1\cdot 6\times 10^{-5}}= \frac{8}{1\cdot 6}\times 10^{-1}= 5\times 10^{-1}=0\cdot 5$
$\displaystyle \therefore 8\times 10^{-6}$ is half of $\displaystyle 1\cdot 6\times 10^{-5}$

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

The thickness of paper is $0.004$ m and that of another paper is $0.008$ m. Compare their sizes.

  1. Paper-1 is double thicker than paper-2.

  2. Thickness of paper-1 is half than paper-2.

  3. Thickness of paper-1 is one-fourth than paper-2.

  4. Paper-1 and paper-2 are both equally thick.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle 0\cdot 004= 4\times 10^{-3}$ m


$\displaystyle 0\cdot 008=8\times 10^{-3}$
Now
$\displaystyle \frac{0\cdot 004}{0\cdot 008}= \frac{4\times 10^{-3}}{8\times 10^{-3}}= \frac{4}{8}= \frac{1}{2}$
$\displaystyle \therefore $ Thickness of paper-1 is half than paper-2

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

Use an appropriate comparison symbol $0.0000486$ _____ $0.00000387$.

  1. $<$
  2. $>$
  3. $=$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle 0.0000486=4\cdot 86\times 10^{-5}$
$\displaystyle 0.00000387=3\cdot 87\times 10^{-6}$
Thus
$\displaystyle 4\cdot 86\times 10^{-5}> 3\cdot 87\times 10^{-6}$

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

If $2^{p + 2} + 2^{p + 1} = 96$, then find the value of $ p$.

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

As given, $2^{p+2}+2^{p+1}=96$
Rewriting the left hand side of equation using $x^a.x^b=x^{a+b}$.
$2^p.2^2+2^p.2^1=96$
$2^p(2^2+2^1)=96$
$2^p\times6=96$
$2^p=16=2^4$
$p=4$
Hence, option D is correct.