Tag: repeated multiplication

Quizzes (8) Questions (6)

Questions Related to repeated multiplication

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

The value of $\displaystyle\frac{2^{m+3}\times3^{2m-n}\times5^{m+n+3}6^{n+1}}{6^{m+1}\times10^{n+3}\times15^m}$ 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

Numerator $=2^{m+3}\cdot3^{2m-n}\cdot5^{m+n+3}\cdot2^{n+1}\cdot3^{n+1}$
$=2^{m+n+4}\cdot3^{2m+1}\cdot5^{m+n+3}$ (i)
Denominator $=2^{m+1}\cdot3^{m+1}\cdot2^{n+3}\cdot5^{n+3}\cdot3^m\cdot5^m$
$=2^{m+n+4}\cdot3^{2m+1}\cdot5^{m+n+3}$ (ii)
Given expression $=1$

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

What is the unit digit in ${({6374}^{1793}\times {625}^{317}\times{341}^{491})}$?

  1. $0$
  2. $2$
  3. $3$
  4. $5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Unit digit in ${6374}^{1993}=$ Unit digit in ${(4)}^{1793}$
=Unit digit in $[{({4}^{2})}^{896}\times 4]$
=Unit digit in $(6\times 4)=4$
Unit digit in ${(625)}^{317}=$ Unit digit in ${(5)}^{317}=5$
Unit digit in ${(341)}^{491}=$ Unit digit in ${(1)}^{491}=1$
Required digit$=$ Unit digit in $(4\times 5\times1)=0$

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

The number of values of $x\ \epsilon \ [0,5]$ at which $f(x)=|x-\dfrac{1}{4}|+|x-2|+\tan{x}$ is not differentiable are

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

The function contains absolute value terms and a trigonometric term. The absolute value expressions are not differentiable at their critical points where the inside equals zero, and tan(x) has discontinuities and points of non-differentiability within the interval [0, 5], culminating in 4 points total.

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

The greatest of the number 
$1,2^{1/2},3^{1/3},4^{1/4},5^{1/5}, 6^{1/6}, and \ 7^{1/7}$ is

  1. $2^1/2$
  2. $3^1/3$
  3. $7^1/7$
  4. $4^1/4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the maximum of x^(1/x), consider the function f(x) = x^(1/x). Its derivative is f'(x) = x^(1/x) * (1 - ln(x)) / x^2. The maximum occurs at x = e (approx 2.718). Comparing values near e, 3^(1/3) is larger than 2^(1/2) and 4^(1/4).

Multiple choice maths repeated multiplication exponentiation index notation and products of prime factors powers

Find the value of $\displaystyle\frac{5^0+5^{-1}}{5^0-5^{-1}}-\left(\frac{8}{27}\right)^{\displaystyle\frac{1}{3}}-\left(\frac{36}{25}\right)^{-\displaystyle\frac{1}{3}}$

  1. 0
  2. $\displaystyle\frac{1}{2}$

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle\frac{\displaystyle1+\frac{1}{5}}{\displaystyle1-\frac{1}{5}}-\left[\left(\frac{2}{3}\right)^3\right]^{\displaystyle\frac{1}{3}}-\left[\left(\frac{6}{5}\right)^2\right]^{\displaystyle-\frac{1}{2}}=\frac{\displaystyle\frac{6}{5}}{\displaystyle\frac{4}{5}}-\left(\frac{2}{3}\right)^1-\left(\frac{6}{5}\right)^{-1}=\frac{6}{4}-\frac{2}{3}-\frac{5}{6}=\frac{18-8-10}{12}=0$