Question 12 Marks
If $m^2=-2$ and $n=2$; find the values of: $m^n+n^m$
Answer
$\begin{aligned} & m^n+n^m \\ & m=-2, n=2 \\ & =(-2)^2+(2)^{-2} \\ & =4+\frac{1}{2} \times \frac{1}{2} \\ & =\frac{4 \times 4}{1 \times 4}+\frac{1}{4} \\ & =\frac{16+1}{4}=\frac{17}{4}=4 \frac{1}{4}\end{aligned}$
View full question & answer→Question 22 Marks
If $m^2=-2$ and $n=2$; find the values of: $m^2+n^2-2 m n$.
Answer$\therefore m ^2+ n ^2-2 mn$
$\text { Put } m =-2, n =2$
$=(-2)^2+(2)^2-2(-2)(2)$
$=4+4-(-8)$
$=8+8$
$=16$
View full question & answer→Question 32 Marks
Evaluate: $5^{\mathrm{n}} \times 25^{\mathrm{n}-1} \div\left(5^{\mathrm{n}-1} \times 25^{\mathrm{n}-1}\right)$
Answer
$\begin{aligned} & 5^{\mathrm{n}} \times 25^{\mathrm{n}-1} \div\left(5^{\mathrm{n}-1} \times 25^{\mathrm{n}-1}\right) \\ & =5^{\mathrm{n}} \times 25^{\mathrm{n}-1} \times \frac{1}{\left(5^{\mathrm{n}-1} \times 25^{\mathrm{n}-1}\right)} \\ & =5^{\mathrm{n}} \times \frac{1}{5^{\mathrm{n}-1}}=5^{\mathrm{n}-\mathrm{n}+1}=5^1\end{aligned}$
View full question & answer→Question 42 Marks
Evaluate: $5^3 \times 3^2+(17)^0 \times 7^3$
Answer$5^3 \times 3^2+(17)^0 \times 7^3$
$=5 \times 5 \times 5 \times 3 \times 3+(17)^0 \times 7 \times 7 \times 7\left(\because a^0=1\right)$
$=125 \times 9+1 \times 343$
$=1125+343=1468$
View full question & answer→Question 52 Marks
Simplify and express the Solution in the positive exponent form:
$\frac{a^{-7} \times b^{-7} \times c^5 \times d^4}{a^3 \times b^{-5} \times c^{-3} \times d^8}$
Answer$\frac{a^{-7} \times b^{-7} \times c^5 \times d^4}{a^3 \times b^{-5} \times c^{-3} \times d^8}$
$=\mathrm{a}^{-7-3} \times \mathrm{b}^{-7+5} \times \mathrm{c}^{5-(-3)} \times \mathrm{d}^{4-8}$
$=\mathrm{a}^{-10} \times \mathrm{b}^{-2} \times \mathrm{c}^8 \times \mathrm{d}^{-4}$
View full question & answer→Question 62 Marks
Simplify, giving Solution with positive index
$(4x^2y^3)^3 ÷ (3x^2y^3)^3$
Answer$\left(4 x^2 y^3\right)^3 \div\left(3 x^2 y^3\right)^3 $
$ =\frac{4^3 x^{2 \times 3} y^{3 \times 3}}{3^3 x^{2 \times 3} y^{3 \times 3}} $
$ =\frac{4^3 x^6 y^9}{3^3 x^6 y^9} $
$=\frac{4^3}{3^3}=\frac{64}{27}$
View full question & answer→Question 72 Marks
Simplify, giving Solution with positive index
$(n^2)^2 (- n^2)^2$
Answer$ \left(n^2\right)^2\left(-n^2\right)^2$
$ =n^{2 \times 2}(-n)^{2 \times 3}=n^4 \times(-n)^6$
$ =-n^4-1^6 n^6 $
$ =-n^{4+6}=-n^{10}$
View full question & answer→Question 82 Marks
Simplify, giving Solution with positive index
$(a^{10})^{10} (1^6)^{10}$
Answer$(a^{10})^{10} (1^6)^{10}$
$= a^{10\times 10} 1^{6\times 10}$
$= a^{100} 1^{60}$
$= a^{100}$
View full question & answer→Question 92 Marks
Simplify, giving Solution with positive index
$4x^2y^2 ÷ 9x^3y^3$
Answer$4 x^2 y^2 \div 9 x^3 y^3$
$=\frac{4 x^2 y^2}{9 x^3 y^3}=\frac{4 x^{2-3} y^{2-3}}{9}$
$=\frac{4 x^{-1} y^{-1}}{9}=\frac{4}{9 x y}$ (Since index should by positive)
View full question & answer→Question 102 Marks
Simplify, giving Solution with positive index
$3^y. 3^2. 3^{-4}$
Answer$3^{y \cdot} \cdot 3^2 \cdot 3^{-4}$
$=3^y \cdot \frac{3^2}{3^4}=3^y=\frac{3 \times 3}{3 \times 3 \times 3 \times 3}$
$=3^y \times \frac{1}{3^2}=3^{y-2}$
View full question & answer→Question 112 Marks
Simplify, giving Solution with positive index
$(-3)^2 (3)^3$
Answer$(-3)^2 (3)^3$
$= (- 1 \times 3)^2.(3)^3$
$= (-1)^2 \times 3^2 . 3^3$
$= -1^2 . 3^{2+3} = 1.3^5 = 3^5$
View full question & answer→Question 122 Marks
Simplify, giving Solution with positive index
$(- y^2) (- y^3)$
Answer$\left(-y^2\right)\left(-y^3\right)$
$=(-1 \times y)^2 \cdot(-1 \times y)^3$
$=(-1)^2 \cdot y^2 \cdot(-1) \times y^3$
$=1^{2+3} \cdot y^{2+3}$
$=1^5 y^5=y^5$
View full question & answer→Question 132 Marks
Simplify, giving Solution with positive index
$(- a^5) (a^2)$
Answer$(- a^5) (a^2)$
$= (-1 \times a)^5 \times a^2$
$= (-1)^5 \times a^{5+2}$
$= - 1 \times a^7 = - a^7$
View full question & answer→Question 142 Marks
Evaluate:$ (3^5 x 4^7 x 5^8)^0$
Answer$\left(3^5 \times 4^7 \times 5^8\right)^0$
$=3^{5 \times 0} \times 4^{7 \times 0} \times 5^{8 \times 0}$
$=3^0 4^0 5^0=1 \times 1 \times 1=1$
View full question & answer→Question 152 Marks
Evaluate: $4^4 ÷ 4^3 x 4^0$
Answer$4^4 \div 4^3 \times 4^0$
$=\frac{4^4}{4^3 4^0}=\frac{4^4}{4^3 \times 1}$
$=\frac{4^4}{4^3}=4^{4-3}=4^1=4$
View full question & answer→Question 162 Marks
Which is greater:
$5^4$ or $4^5$
Answer$5^4$ or $4^5$
Since, $5^4=5 \times 5 \times 5 \times 5=625$
and, $4^5=4 \times 4 \times 4 \times 4 \times 4=1024$
$\because 1024$ is greater than $625$
$ \Rightarrow 4^5>5^4$
View full question & answer→Question 172 Marks
Which is greater:
$4^3$ or $3^4$
Answer$4^3$ or $3^4$
Since, $4^3=4 \times 4 \times 4=64$
and, $3^4=3 \times 3 \times 3 \times 3=81$
$\because 81$ is greater than $64 \Rightarrow 3^4>4^3$
View full question & answer→Question 182 Marks
Which is greater:
$2^5$ or $5^2$
Answer$2^5$ or $5^2$
Since, $2^5=2 \times 2 \times 2 \times 2 \times 2=32$
and, $5^2=5 \times 5=25$
$\because 32$ is greater than $25 \Rightarrow 2^5>5^2$
View full question & answer→Question 192 Marks
Which is greater:
$2^3$ or $3^2$
Answer$2^3 \text { or } 3^2$
Since, $2^3=2 \times 2 \times 2=8$
and, $3^2=3 \times 3=9$
$\because 9$ is greater thah $8 \Rightarrow 3^2>2^3$
View full question & answer→Question 202 Marks
Evaluate: $\left(\frac{3}{5}\right)^2 \times\left(-\frac{2}{3}\right)^3$
Answer
$\begin{aligned} & \left(\frac{3}{5}\right)^2 \times\left(-\frac{2}{3}\right)^3 \\ & =\left(\frac{3}{5}\right) \times\left(\frac{3}{5}\right) \times\left(-\frac{2}{3}\right) \times\left(-\frac{2}{3}\right) \times\left(-\frac{2}{3}\right) \\ & =\frac{9}{25} \times\left(\frac{-8}{27}\right) \\ & =-\frac{8}{75}\end{aligned}$
View full question & answer→Question 212 Marks
Evaluate: $\left(-\frac{3}{4}\right)^3 \times\left(\frac{2}{3}\right)^4$
Answer
$\begin{aligned} & \left(-\frac{3}{4}\right)^3 \times\left(\frac{2}{3}\right)^4 \\ & =\left(-\frac{3}{4}\right) \times\left(-\frac{3}{4}\right) \times\left(-\frac{3}{4}\right) \times\left(\frac{2}{3}\right) \times\left(\frac{2}{3}\right) \times\left(\frac{2}{3}\right) \times\left(\frac{2}{3}\right)\end{aligned}$
$=\frac{-27}{64} \times \frac{16}{81}=-\frac{1}{2}$
View full question & answer→Question 222 Marks
Evaluate: $\left(\frac{2}{3}\right)^3 \times\left(\frac{3}{4}\right)^2$
Answer
$\begin{aligned} & \left(\frac{2}{3}\right)^3 \times\left(\frac{3}{4}\right)^2 \\ & =\left(\frac{2}{3}\right) \times\left(\frac{2}{3}\right) \times\left(\frac{2}{3}\right) \times\left(\frac{3}{4}\right) \times\left(\frac{3}{4}\right) \\ & =\frac{8}{27} \times \frac{9}{16}=\frac{1}{6}\end{aligned}$
View full question & answer→Question 232 Marks
Evaluate: $\left(\frac{3}{4}\right)^4$
Answer
$\begin{aligned} & \left(\frac{3}{4}\right)^4 \\ & =\left(\frac{3}{4}\right) \times\left(\frac{3}{4}\right) \times\left(\frac{3}{4}\right) \times\left(\frac{3}{4}\right) \\ & =\frac{3 \times 3 \times 3 \times 3}{4 \times 4 \times 4 \times 4}=\frac{81}{256}\end{aligned}$
View full question & answer→Question 242 Marks
Evaluate: $(5 x 4)^2$
Answer$(5 x 4)^2 = 5 x 5 x 4 x 4$
$= 25 x 16$
$= 400$
View full question & answer→Question 252 Marks
Evaluate: $(4 x 3)^3$
Answer$(4 x 3)^3 =4 x 4 x 4 x 3 x 3 x 3$
$= 64 x 27$
$= 1728$
View full question & answer→Question 262 Marks
Evaluate: $3^2 x 4^2$
Answer$3^2 x 4^2 =3 x 3 x 4 x 4$
$= 9 x 16$
$=144$
View full question & answer→Question 272 Marks
Evaluate: $5^3 x 2^4$
Answer$5^3 x 2^4= 5 x 5 x 5 x 2 x 2 x 2 x 2$
$= 125 x 16$
$= 2000$
View full question & answer→Question 282 Marks
Evaluate: $3^2 x 5^3$
Answer$3^2 x 5^3 = 3 x3 x 5 x 5 x 5$
$= 9 x 125$
$= 1125$
View full question & answer→Question 292 Marks
Evaluate: $2^2 x 3^3$
Answer$2^2 x 3^3= 2 x 2 x 3 x 3 x 3$
$= 4 x 27$
$= 108$
View full question & answer→Question 302 Marks
Evaluate: $3^3 \times 5^2$
Answer$3^3 \times 5^2==3 \times 3 \times 3 \times 5 \times 5$
$=27 \times 25$
$=675$
View full question & answer→Question 312 Marks
Evaluate: $2^3 \times 5^2$
Answer$2^3 \times 5^2=2 \times 2 \times 2 \times 5 \times 5$
$=8 \times 25$
$=200$
View full question & answer→Question 322 Marks
Evaluate: $2^3 \times 4^2$
Answer$2^3 \times 4^2=$
$=2 \times 2 \times 2 \times 4 \times 4$
$=8 \times 16$
$=128$
View full question & answer→Question 332 Marks
If $64 \times 625 = 2^a \times 5^b$^ ; find: $2^b \times 5^a$
Answer$2^b x 5^a$
$= 2^4 \times 5^6$
$= 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$
$= 16 \times 15625 = 250000$
View full question & answer→