Tag: power and exponent

Quizzes (1) Questions (94)

Questions Related to power and exponent

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

Simplify: $\displaystyle \left ( -a \right )^{9}\times \left ( -b \right )^{9}$ 

  1. $\displaystyle \left ( ab \right )^{9}$
  2. $\displaystyle \left ( -ab \right )^{9}$
  3. $\displaystyle -\left ( ab \right )^{9}$
  4. $\displaystyle \left ( a-b \right )^{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$(-a)^9 \times (-b)^9 = [ -a \times -b]^9$


= $ [ a \times b]^9$

=$ (ab)^9$
So, option $A$ is correct.

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

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

  1. $\displaystyle\left ( \frac{-9}{49} \right )$
  2. $\displaystyle\left ( \frac{9}{49} \right )$
  3. $\displaystyle\left ( \frac{-49}{9} \right )$
  4. $\displaystyle\left ( \frac{49}{9} \right )$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $\displaystyle -\frac{32}{243}$
  2. $\displaystyle \frac{32}{243}$
  3. $\displaystyle -\frac{243}{32}$
  4. $\displaystyle \frac{243}{32}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  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} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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


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

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

Which of the law does not stand true ?

  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. $\displaystyle \frac{a^{m}}{a^{m}}=a^{m}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

  1. $0$
  2. $1$
  3. $x^{a-b-c}$

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

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