Tag: maths

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Questions Related to maths

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

The largest number among the following is

  1. $\displaystyle 3^{2^{2^{2^2}}}$
  2. $\displaystyle \left \{ \left ( 3^{2} \right )^{2} \right \}^{2}$
  3. $\displaystyle 3^{2}\times 3^{2}\times 3^{2}$
  4. $3222$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$1) 3^{2^{2^{2^{2}}}}=3^{2^{2^{4}}}=3^{16}$


$ 2) \left { \left ( 3^{2} \right )^{2} \right }^{2}=3^{8}=6561$

$ 3) 3^{2}\times 3^{2}\times 3^{2}=3^{2+2+2}=3^{6}=729$

$ \therefore 3^{2^{2^{2^{2}}}}>\left { \left ( 3^{2} \right )^{2} \right }^{2}>3222>3^{2}\times 3^{2}\times 3^{2}$

The largest number among the above is $3^{2^{2^{2^{2}}}}$.

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

Evaluate : $\displaystyle \left( \frac{3}{4} \right)^0 \times 2 \frac{1}{4} - \left( 2 \frac{1}{4} \right)^0 \times \frac{3}{4}$--

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

$1 \times \dfrac{9}{4} - 1 \times \dfrac{3}{4}$

$=\dfrac{9}{4} - \dfrac{3}{4}$

$=\dfrac{6}{4}$

$=\dfrac{3}{2}$

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.