Question 1 :
Find the value : <br/>i) $\left(\dfrac{4}{5}\right)^3 \div \left(\dfrac{4}{5}\right)^2$<br/>ii) $4^7 \div 4^5$
Question 2 :
If $x$ be any non-zero integer and $m,n$ be positive integers, then $x^m \times x^n$ is equal to<br/>
Question 3 :
To simplify the following expression correctly, what must be done with the exponents?<br/>${ { 5 }^{ a }\times { 5 }^{ b }\times }{ 5 }^{ c }$<br/>
Question 5 :
If $7^{10}= 7 \times 7^n$, what is the value of $n$?
Question 8 :
Given that $2^h\times 2^3 = 2^9$, find the value of h.
Question 18 :
Simplify the following:<br>${ (-2) }^{ 7 }\times { (-2) }^{ 3 }\times { (-2) }^{ 4 }$
Question 20 :
Simplify:<br>$\left( { 4 }^{ -1 }\times { 3 }^{ -1 } \right) \div { 6 }^{ -1 }$
Question 21 :
Simplify the following:<br>${ \left( \cfrac { 1 }{ 2 } \right) }^{ 4 }\times { \left( \cfrac { 1 }{ 2 } \right) }^{ 5 }\times { \left( \cfrac { 1 }{ 2 } \right) }^{ 6 }$
Question 22 :
Simplify and give reasons:<br>$\left[ { \left( \cfrac { 3 }{ 2 } \right) }^{ -2 } \right] ^{ 2 }$
Question 25 :
<span>Solve:</span><div><br/></div><div>$\displaystyle \dfrac {x^{a(b - c)}}{x^{b(a - c)}} \div (\dfrac {x^b}{x^a})^c = $.</div>
Question 26 :
<span>Express with positive index </span>$\displaystyle \left ( \frac{4}{9} \right )^6 \times \left ( \frac{4}{9} \right )^{-4}$
Question 35 :
If $5^{n} \div 5^{3} = 5^{7}$, then find the value of $n$.
Question 36 :
If $x$ is any non-zero number and $m < n$, then $\displaystyle \frac {x^n}{x^m}$ is
Question 43 :
The seventh root of x divided by the eighth root of x is