Tag: maths

Questions Related to maths

$8^3 \times 8^2 \times 8^{-5}$ is equal to ?

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

  1. $0$

  2. $1$

  3. $8$

  4. $64$

Show answer
Correct Option: B
Explanation:

$={8}^{3+2-5}$

$={8}^{0}$
$={1}$

The largest number among the following is

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

  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. $3222$

Show answer
Correct Option: A
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 $3^{2^{2^{2^{2}}}}$.

If $4^{2x}=\frac {1}{32}$, then the value of x is

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

  1. $\frac {5}{4}$

  2. $-\frac {5}{4}$

  3. $\frac {3}{4}$

  4. $-\frac {5}{2}$

Show answer
Correct Option: B
Explanation:

$4^{2x}=\frac {1}{32}\Rightarrow (2^2)^{2x}=\frac {1}{2^5}$
$\Rightarrow 2^{4x}=2^{-5}$
$\Rightarrow 4x=-5$
$x=\frac {-5}{4}$

$ \displaystyle x^{m}=x^{n}\Rightarrow m =  $

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

  1. $>n$

  2. $=n$

  3. $<n$

  4. None of this

Show answer
Correct Option: B
Explanation:

Given that:

$x^m=x^n$
$\because$ bases are equal in both sides, 
$\therefore$ on comparing the powers, we have
$\Rightarrow m=n$.

The number of digits in the number $N=2^{12}\times5^8$ is

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

  1. $9$

  2. $10$

  3. $11$

  4. $20$

Show answer
Correct Option: B
Explanation:

The factors $2$ and $5$ in the given number are the factors of $10$.
We can write $N$ as-
$ N=2^8\times2^4\times5^8 $
$=2^4(2^8\times5^8)$
$=2^4(10)^8=16\times10^8$
Therefore, the number of digits in $N$ is $10$.

The value of $x^{4/8} \div x^{12/8}$---

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

  1. $x^{4/8}$

  2. $x^{6}$

  3. $\displaystyle \frac{1}{x}$

  4. $x$

Show answer
Correct Option: C
Explanation:

$x^1/2 / x^3/2$


$=x^(1/2-3/2)$

$=x^{-1}$

$=\dfrac{1}{x}$

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

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

  1. $\displaystyle \frac{3}{2}$

  2. $\displaystyle \frac{3}{4}$

  3. $1$

  4. $\displaystyle 2\frac{1}{4}$

Show answer
Correct Option: A
Explanation:

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

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

$=\dfrac{6}{4}$

$=\dfrac{3}{2}$

Find the value of $2 \times 256^{3/4}$---

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

  1. $128$

  2. $\displaystyle \frac{1}{128}$

  3. $-128$

  4. $\displaystyle - \frac{1}{128}$

Show answer
Correct Option: A
Explanation:

correct option is A..

The value of $x^{5/6} \div x^{11/6}$---

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

  1. $\displaystyle \frac{1}{x}$

  2. $x^{1/6}$

  3. $x^6$

  4. $16$

Show answer
Correct Option: A
Explanation:

$=\dfrac {x^{5/6}}{x^{11/6}}$

$=x^{5/6-11/6}$
$=x^{-1}$
$=\dfrac 1x$

Which of the following expresses the power of quotient rule?

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

  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. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{-m}}$

Show answer
Correct Option: A
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.