Question 11 Mark
Evaluate: $\Big(\frac{5}{6}\Big)^{6}\times\Big(\frac{5}{6}\Big)^{-4}$
Answer$\Big(\frac{5}{6}\Big)^{6}\times\Big(\frac{5}{6}\Big)^{-4}$ $=\Big(\frac{5}{6}\Big)^{6-4}$ $=\Big(\frac{5}{6}\Big)^{2}$ $=\frac{5}{6}\times\frac{5}{6}$ $=\frac{25}{36}$
View full question & answer→Question 21 Mark
Write the following numbers in usual form:
$3.74 × 10^5$
Answer$3.74\times10^5$
$=\frac{374}{100}\times10^5$
$=\frac{374}{10^2}\times10^5$
$=374\times1000$
$=374000$
View full question & answer→Question 31 Mark
Evaluate: $\Big(\frac{-2}{3}\Big)^{-5}$
Answer$\Big(\frac{-2}{3}\Big)^{-5}=\Big(\frac{-3}{2}\Big)^{5}$ $=\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)$ $=\frac{-243}{32}$
View full question & answer→Question 41 Mark
Fill in the blank.$\Big(\frac{-2}{3}\Big)^{-2}=\ ......$
Answer$\Big(\frac{-2}{3}\Big)^{-2}=\frac{9}{4}$Solution:
$\Big(\frac{-2}{3}\Big)^{-2}$
$=\Big(\frac{3}{-2}\Big)^{2}$
$=\frac{3^2}{-2^2}$
$=\frac{9}{4}$
View full question & answer→Question 51 Mark
Evaluate: $\Big(\frac{-2}{3}\Big)^{-5}$
Answer$\Big(\frac{-2}{3}\Big)^{-5}$ $=\Big(\frac{3}{-2}\Big)^{5}$ $=\frac{3^{5}}{-2^{5}}$ $=\frac{243}{-32}$ $=\frac{243\times-1}{-32\times-1}$ $=\frac{-243}{32}$
View full question & answer→Question 61 Mark
Fill in the blank.
$5.32 × 10^{-4}$ in usual form is ________.
Answer$5.32\times10^{-4}$
$=\frac{5.32}{10^4}$
$=\frac{5.32}{10000}$
$=0.000532$
View full question & answer→Question 71 Mark
Write the following numbers in standard form:
$168000000$
Answer$168000000$
$= 1.68 × 10^{-8}$
View full question & answer→Question 81 Mark
Write the following numbers in standard form:
$4630000000000$
Answer$4630000000000$
$= 4.63 × 10^12$
View full question & answer→Question 91 Mark
Evaluate: $\Big(\frac{1}{2}\Big)^{-5}$
Answer$\Big(\frac{1}{2}\Big)^{-5}$
$=(2)^5=2\times2\times2\times2\times2$
$=32$
View full question & answer→Question 101 Mark
Fill in the blank.
$0.0000123$ written in standard form is __________.
Answer$0.0000123$ written in standard form is $1.23 × 10^{-5}$.
Solution:
$0.0000123$
$=\frac{123}{10000000}$
$=\frac{123}{10^7}$
$=\frac{1.23\times100}{10^7}$
$=\frac{1.23\times10^2}{10^7}$
$=1.23\times10^{(2-7)}$
$=1.23\times10^{-5}$
View full question & answer→Question 111 Mark
Evaluate: $\Big(\frac{9}{8}\Big)^{-3}\times\Big(\frac{9}{8}\Big)^{2}$
Answer$\Big(\frac{9}{8}\Big)^{-3}\times\Big(\frac{9}{8}\Big)^{2}$ $=\Big(\frac{9}{8}\Big)^{-3+2}$ $=\Big(\frac{9}{8}\Big)^{-1}$$=\frac{8}{9}$
View full question & answer→Question 121 Mark
Evaluate:
$\Big(\frac{5}{7}\Big)^{0}$
Answer $\Big(\frac{5}{7}\Big)^{0}$ Using the property $\Big(\frac{\text{a}}{\text{b}}\Big)^0=1$
We, have:
$\Big(\frac{5}{7}\Big)^{0}=1$
View full question & answer→Question 131 Mark
Write the following numbers in standard form:
$345 × 10^5$
Answer$345 × 10^5$
$=3.45 × 10^2 × 10^5$
$= 3.45 × 10^7$
View full question & answer→Question 141 Mark
The height of Mount Everest is $8848m.$ Write it in standard form.
AnswerHeight of Mount Everest $= 8848m$
$= 8.848 \times 1000$
$= 8.848 \times 10^3$
View full question & answer→Question 151 Mark
The distance from the earth to the sun is $149600000000m.$ Write it in standard form.
AnswerDistance between the earth and the sun $= 149600000000m$
$= (1.49600000000 × 100000000000)m$
$= (1.496 × 10^11)m$
View full question & answer→Question 161 Mark
Evaluate: $\Big(\frac{5}{3}\Big)^{2}\times\Big(\frac{5}{3}\Big)^{2}$
Answer$\Big(\frac{5}{3}\Big)^{2}\times\Big(\frac{5}{3}\Big)^{2}$ $=\Big(\frac{5}{3}\Big)^{2+2}$ $=\Big(\frac{5}{3}\Big)^{4}$ $=\frac{5}{3}\times\frac{5}{3}\times\frac{5}{3}\times\frac{5}{3}$ $=\frac{625}{81}$
View full question & answer→Question 171 Mark
Fill in the blank.
$3 × 10^{-3}$ in usual form is ________.
Answer$3 × 10^{-3}$ in usual form is $0.003$.
Solution:
$3\times10^{-3}$
$=\frac{3}{10^3}$
$=\frac{3}{1000}$
$=0.003$
View full question & answer→MCQ 181 Mark
Mark $(\checkmark)$ against the correct answer of the following : If $\Big(\frac{5}{12}\Big)^{-4}\times\Big(\frac{5}{12}\Big)^{3\text{x}}=\Big(\frac{5}{12}\Big)^5$, then $x = ?$
Answer$\Big(\frac{5}{12}\Big)^{-4}\times\Big(\frac{5}{12}\Big)^{3\text{x}}=\Big(\frac{5}{12}\Big)^5$
$\Rightarrow\Big(\frac{5}{12}\Big)^{-4+3\text{x}}=\Big(\frac{5}{12}\Big)^5$
$\Rightarrow-4+3\text{x}=5$
$\Rightarrow3\text{x}=5+4=9$
$\Rightarrow\text{x}=\frac{9}{3}$
$\Rightarrow\text{x}=3$
View full question & answer→Question 191 Mark
Write the following numbers in standard form:
$273000$
Answer$273000$
$= 2.73 × 10^5$
View full question & answer→Question 201 Mark
Evaluate:
$4^{-3}$
Answer$4^{-3}=\Big(\frac{1}{4}\Big)^3$
$=\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}$
$=\frac{1}{64}$
View full question & answer→Question 211 Mark
Express the following in standard form: $0.000003$
Answer$0.000003$$=\frac{3}{1000000}$
$=3\times10^{-6}$
View full question & answer→Question 221 Mark
Write the following numbers in standard form:
$57.36$
Answer$57.36$
$= 5.736 × 10^1$
View full question & answer→Question 231 Mark
Evaluate: $\Big(\frac{3}{4}\Big)^{-2}$
Answer$\Big(\frac{3}{4}\Big)^{-2}$ $=\Big(\frac{4}{3}\Big)^{2}$ $=\Big(\frac{4^2}{3^2}\Big)$ $=\frac{16}{9}$
View full question & answer→Question 241 Mark
Evaluate:
$\Big(\frac{2}{3}\Big)^{-3}\times\Big(\frac{2}{3}\Big)^{-2}$
Answer $\Big(\frac{2}{3}\Big)^{-3}\times\Big(\frac{2}{3}\Big)^{-2}$
$=\Big(\frac{3}{2}\Big)^{3}\times\Big(\frac{3}{2}\Big)^{2}$
$=\Big(\frac{3}{2}\Big)^{3+2}$
$=\Big(\frac{3}{2}\Big)^{5}$
$=\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}$
$=\frac{243}{32}$
View full question & answer→Question 251 Mark
Evaluate:
$3^{-4}$
Answer$3^{-4}$
$=\frac{1}{3^4}$
$=\frac{1}{81}$
View full question & answer→Question 261 Mark
Write the following numbers in standard form:
$3500000$
Answer$3500000$
$= 3.5 \times 10^6$
View full question & answer→Question 271 Mark
Fill in the blank.
$360000$ written in standard form is _________.
Answer$360000 = 3.6 \times 10^4$
$ =3.6 \times 10 \times 10^ 4$
$=3.6 \times 10^{(1+4)} $
$=36 \times 10^5$
View full question & answer→MCQ 281 Mark
Tick $(\checkmark)$ the correct answer the following: $\Bigg[\bigg\{\Big(-\frac{1}{2}\Big)^2\bigg\}^{-2}\Bigg]=\ ?$
- ✓
$\frac{1}{16}$
- B
$16$
- C
$-\frac{1}{16}$
- D
$-16$
AnswerCorrect option: A. $\frac{1}{16}$
$\Bigg[\bigg\{\Big(-\frac{1}{2}\Big)^2\bigg\}^{-2}\Bigg]$
$=\Big(\frac{-1}{2}\Big)^{2\times(-2)(-1)}$
$=\Big(\frac{-1}{2}\Big)^4$
$=\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)$
$=\frac{1}{16}$
View full question & answer→Question 291 Mark
Express the following in standard form:
$345$
Answer$345$
$=3.45 \times 100$
$ =3.45 \times 10^2$
View full question & answer→Question 301 Mark
Evaluate:
$(-4)^3$
Answer$(-4)^3$
$=(-1)^3\times(4)^3$
$=-1\times64$
$=-64$
View full question & answer→Question 311 Mark
Evaluate:
$\Big(\frac{4}{3}\Big)^{-3}$
Answer $\Big(\frac{4}{3}\Big)^{-3}$
$=\Big(\frac{3}{4}\Big)^{3}$
$=\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4}$
$=\frac{27}{64}$
View full question & answer→Question 321 Mark
The speed of light is $300000000m/ sec$. Express it in standard form.
AnswerSpeed of Light $= 300000000m/ sec$
$= 3.00000000 × 100000000$
$= (3 × 10^8)m/ sec$
View full question & answer→Question 331 Mark
Evaluate:
$(-3)^{-4}$
Answer$(-3)^{-4}=\Big(\frac{1}{-3}\Big)^{4}$
$=\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)$
$=\frac{1}{81}$
View full question & answer→