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

Which of the following expresses the power of quotient rule?

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

If the division of two bases is powered by the same exponent,

 then the result is division of both the bases, 
each powered by the given exponent.
$\therefore \left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$
So, option $A$ is correct.

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

Which of the following represents the power of product rule?

  1. $(x\times y)^{a} = x^{a} \times y$
  2. $(x\times y)^{a} = x \times y^{a}$
  3. $(x\times y)^{a} = x^{a} + y^{a}$
  4. $(x\times y)^{a} = x^{a} \times y^{a}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the product of the bases is powered  by the same exponent, 

then the result is multiplication of all the bases, 
each powered by the given exponent.
$\therefore (x\times y)^{a} = x^{a} \times y^{a}$.
So, option $D$ is correct.

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

On simplifying  $\displaystyle 3^{3}\times a^{3}\times b^{3}$, we get

  1. $\displaystyle \left ( 3ab \right )^{3} $
  2. $\displaystyle 3\left ( ab \right )^{3} $
  3. $\displaystyle \left ( 27ab \right )^{3} $

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

$\displaystyle 3^{2}\times a^{3}\times b^{3}=\left ( 3ab \right )^{3}$.

This is the power of product law of exponents.
So, option $A$ is correct.

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

Find the value of: $\displaystyle \left [ \left ( -1 \right )^{2}\times \left ( -1 \right )^{3}\times \left ( -1 \right )^{4} \right ]^{6}$

  1. $3$
  2. $-1$
  3. $1$
  4. $\displaystyle 3^{6}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \left [ \left ( -1 \right )^{2}\times \left ( -1 \right )^{3}\times \left ( -1 \right )^{4} \right ]^{6}$

=$\displaystyle \left [ \left ( -1 \right )^{12}\times \left ( -1 \right )^{18}\times \left ( -1 \right )^{24} \right ]$
=$\displaystyle \left [ 1\times 1\times 1 \right ]$ =$1$
So, option $C$ is correct.

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

The value of $\displaystyle \left (-4  \right ) ^{3}\times \left ( -3 \right )^{3}$ is _____?

  1. $\displaystyle 12^{3}$
  2. $\displaystyle -12^{3}$
  3. $\displaystyle -7^{3}$
  4. $\displaystyle 7^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \left ( -4 \right )^{3}\times \left ( -3 \right )^{3}=\left ( -4\times -3 \right )^{3}$

$=\displaystyle \left ( -4\times -3 \right )^{3}$
$=\displaystyle 12^3$

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

Find the expression which equals $\displaystyle a^{x}\times b^{x}$.

  1. $\left [\displaystyle a^{x}+ b^{x} \right ]$
  2. $\displaystyle \left ( ab\right )^x $
  3. $\displaystyle \left (a+b \right )^{x} $
  4. $\displaystyle a\left ( b \right )^{x} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle a^{x}\times b^{x}=\left ( ab \right )^{n}$

So, option $B$ is correct.

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

Evaluate: $\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}}\times \left ( 5 \right )^{\tfrac{1}{5}} \right ]^{0}$

  1. $40$
  2. $0$
  3. $1$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

=$\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}} \times \left ( 5 \right )^{\tfrac{1}{2}}\right ]^{0}$

=$\displaystyle 4^{0}\times 2^{0}\times 5^{0}$
=$\displaystyle 1\times 1\times 1$
=$1$
So, option $C$ is correct.

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

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

  1. $\displaystyle -\frac{2}{5}$
  2. $\displaystyle -\frac{32}{3125}$
  3. $\displaystyle\frac{64}{15625}$
  4. $\displaystyle -\frac{64}{15625}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \left [ \left ( \frac{-2}{5} \right )^{3} \right ]^{2}=\left ( \frac{-2}{5} \right )^{6}=\frac{\left ( -2 \right )^{6}}{5^{6}}=\frac{64}{15625}$

Hence, option $C$ is correct.