Tag: laws of exponents and powers

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Questions Related to laws of exponents and powers

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