Tag: maths

Questions Related to maths

Evaluate $\displaystyle\left [ \left ( \frac{-3}{7} \right )^{-1} \right ]^{2}$

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $\displaystyle\left ( \frac{-9}{49} \right )$

  2. $\displaystyle\left ( \frac{9}{49} \right )$

  3. $\displaystyle\left ( \frac{-49}{9} \right )$

  4. $\displaystyle\left ( \frac{49}{9} \right )$

Show answer
Correct Option: D
Explanation:

$\displaystyle\left [ \frac{-3}{7} ^{-1}\right ]^{2}=\left [ \left ( \frac{-7}{3} \right )^{1} \right ]^{2}=\left ( \frac{-7}{3} \right )^{2}=\frac{49}{9}$

Hence, option $D$ is correct.

The value of $\displaystyle \left ( \frac{2}{3}\right )^{-5}$ is:

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $\displaystyle -\frac{32}{243}$

  2. $\displaystyle \frac{32}{243}$

  3. $\displaystyle -\frac{243}{32}$

  4. $\displaystyle \frac{243}{32}$

Show answer
Correct Option: D
Explanation:

$\displaystyle\left ( \frac{2}{3} \right )^{-5}=\left ( \frac{3}{2} \right )^{5}=\frac{3^{5}}{2^{5}}=\frac{243}{32}$

Hence, option $D$ is correct.

$\displaystyle \left ( 16\div 15 \right )^{3}$ can also be expressed as:

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $\displaystyle 16^{3}\div 15^{3} $

  2. $\displaystyle 16^{3}\div 15 $

  3. $\displaystyle 16\div 15^{3} $

  4. $\displaystyle 15^{3}\div 16^{3} $

Show answer
Correct Option: A
Explanation:

$\displaystyle\left ( 16\div 15 \right )^{3}=16^{3}\div 15^{3}$ 


This is quotient law of exponents.
Hence, option $A$ is correct

Which of the law does not stand true ?

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$

  2. $\displaystyle \left ( \frac{a^{m}}{a^{n}} \right )^{x}=\frac{a^{mx}}{a^{nx}}$

  3. $\displaystyle \frac{a^{m}}{b^{m}}=\left ( \frac{a}{b} \right )^{m}$

  4. $\displaystyle \frac{a^{m}}{a^{m}}=a^{m}$

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac{a^{m}}{a^{m}}=1$
$\displaystyle\therefore  \frac{a^{m}}{a^{m}}\neq a^{m}$

Which of the following expressions is equivalent to $x^3x^5$?

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $2x^8$

  2. $x^{15}$

  3. $x^2$

  4. $x^8$

  5. $2x^{15}$

Show answer
Correct Option: D
Explanation:

We know, $x^a \times x^b=x^{(a+b)}$
Therefore the value of ${x}^{3}{x}^{5} = {x}^{3+5} = {x}^{8}$

A number when divided by $296$ leaves $75$ as remainder. When the same number is divided by $37$, the remainder will be:

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $1$

  2. $2$

  3. $8$

  4. $11$

Show answer
Correct Option: A
Explanation:

Let $x=296q+75$
$=(37\times 8q+37\times 2)+1$
$=37(8q+2)+1$
Thus, when the number is divided by $37$, the remainder is $1$.

$n$ is a whole number which when divided by $4$ given $3$ as remainder. What will be the remainder when $2n$ is divided by $4$?

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $3$

  2. $2$

  3. $1$

  4. $0$

Show answer
Correct Option: B
Explanation:

Let $n=4q+3$. Then $2n=8q+6=4(2q+1)+2$
Thus, when $2n$ is divided by $4$, the remainder is $2$.

$\dfrac{1}{1+x^{(b-a)}+x^{(c-a)}}+\dfrac{1}{1+x^{(a-b)}+x^{(c-b)}}+\dfrac{1}{1+x^{(b-c)}+x^{(a-c)}} = ?$

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $0$

  2. $1$

  3. $x^{a-b-c}$

  4. None of these

Show answer
Correct Option: B
Explanation:

Given Exp. = $\dfrac{1}{\begin{pmatrix}1+\dfrac{x^b}{x^a}+\dfrac{x^c}{x^a}\end{pmatrix}} + \dfrac{1}{\begin{pmatrix}1+\dfrac{x^a}{x^b}+\dfrac{x^c}{x^b}\end{pmatrix}} + \dfrac{1}{\begin{pmatrix}1+\dfrac{x^b}{x^c}+\dfrac{x^a}{x^c}\end{pmatrix}}$
$= \dfrac{x^a}{(x^a+x^b+x^c)}+\dfrac{x^b}{(x^a+x^b+x^c)} + \dfrac{x^c}{(x^a+x^b+x^c)}$
$= \dfrac{x^a+x^b+x^c}{(x^a+x^b+x^c)}$
$= 1.$

The value of $[(10)^{150}\div (10)^{146}]$

maths power and exponent power of powers laws of exponents and powers law of indices

  1. $1000$

  2. $10000$

  3. $100000$

  4. $10^6$

Show answer
Correct Option: B
Explanation:

$(10)^{150}\div (10)^{146} = \dfrac{10^{150}}{10^{146}}$
$= 10^{150-146}$
$= 10^4$
$= 10000.$

$(256)^{0.16}\times (256)^{0.09} = ?$

maths power and exponent power of powers laws of exponents and powers law of indices

  1. 4

  2. 16

  3. 64

  4. 256.25

Show answer
Correct Option: A
Explanation:

$(256)^{0.16}\times (256)^{0.09} = (256)^{(0.16+0.09)}$
$= (256)^{0.25}$
$= (256)^{(25/100)}$
$= (256)^{(1/4)}$
$= (4^4)^{(1/4)}$
$= 4^{4(1/4)}$
$= 4^1$
$= 4$