Tag: law of indices

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Questions Related to law of indices

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

The value of $\dfrac { { 2 }^{ m+3 }\times { 3 }^{ 2m-n }\times { 5 }^{ m+n+3 }\times { 6 }^{ n+1 } }{ { 6 }^{ m+1 }\times { 10 }^{ n+3 }\times { 15 }^{ m } } $ is equal to 

  1. $0$
  2. $1$
  3. $2^ {m}$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Now,

$\dfrac { { 2 }^{ m+3 }\times { 3 }^{ 2m-n }\times { 5 }^{ m+n+3 }\times { 6 }^{ n+1 } }{ { 6 }^{ m+1 }\times { 10 }^{ n+3 }\times { 15 }^{ m } } $ 
$=\dfrac { { 2 }^{ m+3 }\times { 3 }^{ 2m-n }\times { 5 }^{ m+n+3 }\times(2^{n+1}\times { 3 }^{ n+1 }) }{ (2^{m+1}\times { 3 }^{ m+1 })\times (2^{n+3}\times { 5 }^{ n+3 })\times (3^{m}\times { 5 }^{ m }) } $ 
$=\dfrac { { 2 }^{ m+n+4 }\times { 3 }^{ 2m+1 }\times { 5 }^{ m+n+3 } }{ { 2 }^{ m+n+4 }\times { 3 }^{ 2m+1 }\times { 5 }^{ mm+n+3 } } $ 
$=1$.

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

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

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

$=\dfrac{6}{4}$

$=\dfrac{3}{2}$