Question 4 :
The cubes of all even number between 1 and 5 are .........

Question 6 :
<span>State true or false</span><div>A perfect cube does not end with two zeros</div>

Question 11 :
The value of $\dfrac {2^{2001} + 2^{1999}}{2^{2000} - 2^{1998}}$, is __________.

Question 12 :
Match the following provided that $a$ and $b$ any two rational numbers different from zero and $x, y$ are any two rational numbers.<table class="wysiwyg-table"><tbody><tr><td>$(1)$</td><td>$a^{x} \times a^{y}$<br></td><td>$(a)$</td><td>$a^{x - y}$</td></tr><tr><td>$(2)$</td><td>$a^{x} \div a^{y}$</td><td>$(b)$</td><td>$a^{xy}$</td></tr><tr><td>$(3)$</td><td>$(a^{x})^{y}$</td><td>$(c)$</td><td>$a^{x + y}$</td></tr><tr><td>$(4)$</td><td>$(ab)^{x}$</td><td>$(d)$</td><td>$\dfrac {a^{x}}{b^{x}}$</td></tr><tr><td>$(5)$</td><td>$\left (\dfrac {a}{b}\right )^{x}$</td><td>$(e)$</td><td>$a^{x}\times b^{x}$</td></tr></tbody></table>

Question 14 :
If $x = 2$ and $y = 3$, then find the value of $\left[ \displaystyle\frac { 1 }{ x^{ x } } +\displaystyle\frac { 1 }{ y^{ y } } \right] $<br>

Question 16 :
If $\displaystyle c={ a }^{ 3 }-{ b }^{ 3 },$ then is $c$ a perfect cube?

Question 17 :
Which of the following values are equal?<br>(P) $1^{4}$ (Q) $4^{\circ}$ (R) $0^{4}$ (S) $4^{1}$.

Question 18 :
The value of $ \left\{ \sqrt[4] { \left( \dfrac{1}{x} \right) }^{-12} \right\}^{- \frac{2}{3}} , $ when $x=9$ is :

Question 19 :
Choose the correct answer from the given four options:<br>If $2^3+1^3=3^x$, then the value of $x$ is:<br><br>

Question 20 :
Simplify:<br/><br/>$\displaystyle \frac{\left ( 6.25 \right )^{\frac{1}{2}}\times \left ( 0.0144 \right )^{\frac{1}{2}}+1}{\left ( 0.027 \right )^{\frac{1}{3}}\times \left ( 81 \right )^{\frac{1}{4}}}$<br/>

Question 21 :
Evaluate the given expressions:<br/>${ 125 }^{ \frac { 2 }{ 3 } }$

Question 22 :
Write the correct answer from the given four options.<br>If m is the cube root of n, then n is

Question 24 :
If $\omega (\neq 1)$ is a cube root of unity, and $(1+\omega)^7=A+B\omega$. Then (A, B) equals?

Question 25 :
If $\displaystyle 3^{x+8}=27^{2x+1}$, then the value of<br/>$\displaystyle \left [ \left ( \frac{\sqrt{289}}{\sqrt[3]{216}} \right )^{x}\div \left ( \frac{17}{\sqrt[4]{1296}} \right )^{x} \right ]^{\frac{1}{2}}$ is<br/>

Question 29 :
<span>State whether true or false:</span><div>If $256 = 16^{n}$ then $n = 2$.</div>

Question 31 :
If $\displaystyle x^{5} + 1 = 7777$ and $\displaystyle y^{4} - 1 = 9999$ then find the value of $xy$ where both $x$ and $y$ are positive integers

Question 32 :
Value of $\displaystyle 2^{4}\times \left ( -3 \right )^{2}\times 4^{2}\times \left ( -5 \right )^{2}$ is

Question 34 :
If $a = x^{1/3} - x^{-1/3}, $ then $(a^{3} + 3a)$ is equal to<br/>

Question 35 :
Find the cube of $\displaystyle 2.3\times { 10 }^{ 7 }$.<br/>

Question 36 :
<div>State true or false:</div>A perfect cube may end with two zeros.

Question 38 :
Choose the correct answer from the alternatives given.<br>If $x \, = \, 2^{\frac{1}{3}} \, + \, 2^{\frac{-1}{3}}$ then the value of $2x^3 \, - \, 6x$ will be

Question 39 :
State true or false:<div>There is no perfect cube which ends with $8$.</div>

Question 40 :
<div><div>State true or false:</div></div><div><span>If a number ends with $5$, then its cube ends with $5$.</span><br/></div>