Question 1 :
State True or False.$(27)^{\frac{2}{3}} \div (\dfrac{81}{16})^{-\frac{1}{4}} $ is equal to $13\dfrac{1}{2} $.<br/>
Question 2 :
State true or false<br/>$\displaystyle (8x^3 \div 125y^3)^{\frac {2}{3}}$, then answer is $\displaystyle \frac {4x^2}{25y^2}$<br/>
Question 6 :
The value of $\left (\left (\left (\left (4\right )^{2}\right )^{1/2}\right )^{2}\right )^{1/2}$ is ________.
Question 7 :
State true or false:$\displaystyle (\cfrac {27}{8})^{\tfrac {2}{3}} - (\cfrac {1}{4})^{-2} + 5^0=$ $\displaystyle - \cfrac {51}{4}$<br/>
Question 8 :
State true or false$\displaystyle (a + b)^{-1} . (a^{-1} + b^{-1})$, then answer is $\displaystyle \dfrac {1}{ab^2}$<br/>
Question 13 :
State true or false.$\displaystyle \left(\frac {16}{81}\right)^{-\frac {3}{4}} \times \left(\frac {49}{9}\right)^{\frac {3}{2}} \div \left(\frac {343}{216}\right)^{\frac {2}{3}}$ is equal to $31.5$
Question 15 :
$\displaystyle \left [ \left ( -2 \right )^{4}-\left ( 11-1 \right )\right ]\div 3$
Question 18 :
$4^{3} + 4^{3} + 4^{3} + 4^{3} = 2^{x}$<br/>In the equation above, calculate the value of $x$.<br/>
Question 19 :
If $4^{n-2} + 4^{2} = 32$, then what is the value of $n$?
Question 21 :
What is the smallest integer n for which $\displaystyle { 25 }^{ n }>{ 5 }^{ 12 }$?
Question 23 :
If $\sqrt { { 2 }^{ x } } =16$, then $x=$
Question 31 :
The number of real solutions of the equation (5 + 2$\sqrt6)$ <br> $^{x^2 - 3}$ +(5 - 2$\sqrt6)$ <br> $^{x^2 - 3}$ = 10 is
Question 32 :
If $n$ and $k$ are positive integers and $8^n=2^k$, what is the value of $\dfrac{n}{k}$?
Question 33 :
After simplication $\displaystyle (243)^{-\frac {3}{5}}$, then answer is $\displaystyle \frac {1}{27}$<br/>State true or false:
Question 34 :
If $64^{x} = 4^{x^{2} - 4}$, then find the value of $x$.
Question 35 :
If $(6)^{15} \, \times \, (10)^5 \, \times \,(15)^6 \, = \, 2^x \, \times \, 3^y \, \times \, 5^z$ then find the value of x + y + z. <br/>
Question 41 :
If $x=\dfrac{4}{(\sqrt{5}+1)(\sqrt [ 4 ]{ 5 } +1)(\sqrt [ 8 ]{ 5 } +1)(\sqrt [ 16 ]{ 5 } +1)}$. Then the value of $(1+x)^{48}$ is
Question 42 :
If 9$^{x+2}$= 240 + 9$^{x}$ then the value of x is:
Question 43 :
If $x$ is a positive integer satisfying $x^7=k$ and $x^9=m$, which of the following must be equal to $x^{11}$?<br>
Question 45 :
State whether true or false:If $256 = 16^{n}$ then $n = 2$.
Question 46 :
The average distance between the Sun and a certainplanet is approximately $\displaystyle 2.3\times { 10 }^{ 14 }$inches. Whichof the following is closest to the average distancebetween the Sun and the planet, in kilometers?(1 kilometer is approximately $\displaystyle 3.9\times { 10 }^{ 4 }$ inches )
Question 49 :
If $z=\alpha\sin\theta+\beta\cos\theta$, where $\alpha$ and $\beta$ are positive constants. The maximum value of $z$ is
Question 50 :
Let $f(x)=x^{100}$. If $f(x)$ is divided by $x^{2}+x,$ then the remainder is $r(x)$.Find the value of $r(5)$?<br>
Question 51 :
$\dfrac{2^{n + 4} - 2 \times 2^n}{2 \times 2^{n + 3}} + 2^{-3} = $ ?
Question 53 :
If $a , b , c$ and $d$ are natural numbers such that $a ^ { 3 } = b ^ { 6 } , c ^ { 3 } = d ^ { 4 } ,$ and $d - a = 61 ,$ then thesmallest value of $c - b$ is:
Question 56 :
If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k < -1$, find the value of $k$.
Question 57 :
If $2^a = 3^b = 6^c$ then C cannot be equal to