Tag: use of exponents

Questions Related to use of exponents

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

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

  1. $<$

  2. $>$

  3. $=$

  4. None of these

Show answer
Correct Option: A
Explanation:

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

$0.000008$ _______ $0.000016$

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

  1. is half of

  2. is double than

  3. is one-fourth of

  4. is one-third of

Show answer
Correct Option: A
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 $\displaystyle 1\cdot 6\times 10^{-5}$

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

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

  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.

Show answer
Correct Option: B
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

Compare the folllowing:

$0.000000038$ _______ $\displaystyle 3\cdot 8\times 10^{-8}$

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

  1. $<$

  2. $>$

  3. $=$

  4. None of these

Show answer
Correct Option: C
Explanation:

$\displaystyle 0\cdot 000000038= 3\cdot 8\times 10^{-8}$

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

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

  1. $<$

  2. $>$

  3. $=$

  4. None of these

Show answer
Correct Option: B
Explanation:

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

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

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$

Show answer
Correct Option: D
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.

If $8^x = 16^{x-1}$, find $x $.

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

  1. $\dfrac{1}{8}$

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

  3. $2$

  4. $4$

Show answer
Correct Option: D
Explanation:

Given, $8^x=(16)^{x-1}$

Left hand side, $8^x=(2^3)^x=2^{3x}$
Right hand side $16^{x-1}=(2^4)^{x-1}=2^{4(x-1)}=2^{(4x-4)}$
Equating both sides, we get
$2^{3x}=2^{{4x-4}}$
As bases are equal, then powers must be equal, so
$\Rightarrow 3x=4x-4$
$ \Rightarrow x=4$

If $a^{b} = 4  -ab$ and $b^{a} = 1$, where $a$ and $b$ are positive integers, find $a$.

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

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: C
Explanation:
Plug in real numbers for $a$ and $b$. Since it isn’t clear what numbers to plug in to satisfy the first equation, look at the second equation instead. First, realize that  $a$  cannot be  $0$  since a is a positive integer.
Since, $a\neq0$, so the only way to get $b^a=1$ is if $b=1 $(As $1$ to any power is $1$).
Plugging $b=1$ in to the first equation,
$a^b=4-ab$
$a^1=4-a\times1$
$a=4-a$
$a=2$
Hence, option C is correct.

If $9^n = 27^{n+1}$, then calculate the value of $2^n $.

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

  1. $-\dfrac{10}{3}$

  2. $-\dfrac{8}{3}$

  3. $-\dfrac{3}{8}$

  4. $\dfrac{1}{8}$

  5. $\dfrac{3}{8}$

Show answer
Correct Option: D
Explanation:

Given ${ 9 }^{ n }={ 27 }^{ n+1 }$, which implies
$ { 3 }^{ 2n }={ 3 }^{ 3n+3 }$
Now compare powers, we get
$2n = 3n+3$ , which implies $n = -3$
Therefore ${ 2 }^{ n }={ 2 }^{ -3 }=\dfrac { 1 }{ 8 } $

If $4^{2x + 2} = 64$, 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. $\dfrac {3}{2}$

  4. $2$

Show answer
Correct Option: A
Explanation:

Given is $4^{2x+2}=64$

LHS: 
$\Rightarrow 4^{ 2x+2 }=(2^{ 2 })^{ 2x+2 }\ \Rightarrow { 2 }^{ 4x+4 }$
RHS: 
$\Rightarrow 64=2^6$

Now, LHS $=$ RHS
$\Rightarrow { 2 }^{ 4x+4 }={ 2 }^{ 6 }$
As bases are equal, so powers must be equal,
$\Rightarrow 6=4x+4$
$\Rightarrow 4x=2\ \Rightarrow x=\dfrac { 1 }{ 2 } $