Question 11 Mark
Express the following rational numbers with a positive exponent:
$\bigg[\Big(\frac{4}{3}\Big)^{-3}\bigg]^4$
Answer$\bigg[\Big(\frac{4}{3}\Big)^{-3}\bigg]^4=\Big(\frac{4}{3}\Big)^{(-3)\times(-4)}$
$=\Big(\frac{4}{3}\Big) ^{12}$
View full question & answer→Question 21 Mark
Find the values of the following.
$(3^°+4^{-1})\times2^2$
Answer$(3^°+4^{-1})\times2^2=\Big(1+\frac{1}{4}\Big)\times4$
$\Big(\because\text{a}^°=1\text{m},\text{a}^{-\text{m}}=\frac{1}{\text{m}}\Big)$
$=\frac{4+1}{4}\times4=\frac{5}{4}\times4=5$
View full question & answer→Question 31 Mark
Express the following rational numbers with a positive exponent:
$4^3\times4^{-9}$
Answer$4^3\times4^{-9}=4^{3-9}=4^{-6}=\Big(\frac{1}{4}\Big)^6$
View full question & answer→Question 41 Mark
Evaluate:
$(-3)^{-2}$
Answer$(-3)^{-2}$
$=\frac{1}{(-3)^2}=\frac{1}{(-3)\times(-3)}=\frac{1}{9}$
View full question & answer→Question 51 Mark
Express of the following as a rational number in the form $\frac{\text{p}}{\text{q}}:$
$(-7)^{-1}$
Answer$(-7)^{-1}=\frac{-1}{7}$
View full question & answer→Question 61 Mark
Simplify:$(5^{-1}\div6^{-1})^3$
Answer$(5^{-1}\div6^{-1})^3$
$=\Big(\frac{1}{5}\div\frac{1}{6}\Big)^3=\Big(\frac{1}{5}\times\frac{6}{1}\Big)^3$
$=\Big(\frac{6}{5}\Big)^3=\frac{6\times6\times6}{5\times5\times5}=\frac{216}{125}$
View full question & answer→Question 71 Mark
Express of the following rational numbers with a negative exponent:
$\Big (\frac{3}{5}\Big)^{4}$
Answer$\Big (\frac{3}{5}\Big)^{4}=\Big(\frac{5}{3}\Big)^{-4}$
View full question & answer→Question 81 Mark
Express of the following rational numbers with a negative exponent:
$\bigg[\Big(\frac{3}{2}\Big)^4\bigg]^{-3}$
Answer$\bigg[\Big(\frac{3}{2}\Big)^4\bigg]^{-3}=\Big(\frac{3}{2}\Big)^{4\times(-3)}=\Big(\frac{3}{2}\Big)^{-12}$
View full question & answer→Question 91 Mark
Express the following rational numbers with a positive exponent:
$\bigg[\Big(\frac{3}{2}\Big)^{4}\bigg]^{-2}$
Answer$\bigg[\Big(\frac{3}{2}\Big)^{4}\bigg]^{-2}=\Big(\frac{3}{2}\Big)^{(4)\times(-2)}$
$=\Big(\frac{3}{2}\Big) ^{12}=\Big(\frac{2}{3}\Big)^8$
View full question & answer→Question 101 Mark
Find the values of the following.
$3^{-1}+4^{-1}$
Answer$3^{-1}+4^{-1}=\frac{1}{3}+\frac{1}{4}$
$=\frac{4+3}{12}=\frac{7}{12}$
View full question & answer→Question 111 Mark
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0:$
$\Big(\frac{1}{2}\Big)^{-5}$
Answer$\Big(\frac{1}{2}\Big)^{-5}=\Big(\frac{2}{1}\Big)^5$
$=2\times2\times2\times2\times2=32$
View full question & answer→Question 121 Mark
Evaluate:
$\Big( \frac{-1}{2}\Big)^{-1}$
Answer$\Big( \frac{-1}{2}\Big)^{-1}$
$=\Big( \frac{-1}{2}\Big)^{-4}=(-2)^1=-2$
View full question & answer→Question 131 Mark
Write the following in exponential form:
$\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}$
Answer$\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}\times\Big(\frac{3}{2}\Big)^{-1}$
$\Big(\frac{3}{2}\Big)^{-1+(-1)+(-1)+(-1)}$
$=\Big(\frac{3}{2}\Big)^{-4}$
View full question & answer→Question 141 Mark
Express of the following as a rational number in the form $\frac{\text{p}}{\text{q}}:$
$\Big(\frac{3}{5}\Big)^{-1}\times\Big(\frac{5}{2}\Big)^{-1}$
Answer$\Big(\frac{3}{5}\Big)^{-1}\times\Big(\frac{5}{2}\Big)^{-1}=\Big(\frac{5}{3}\Big)^{1}\times\Big(\frac{2}{5}\Big)^{1}$
$=\frac{5}{3}\times\frac{2}{5}=\frac{2}{3}$
View full question & answer→Question 151 Mark
Express of the following as a rational number in the form $\frac{\text{p}}{\text{q}}:$
$\Big(\frac{1}{4}\Big)^{-1}$
Answer$\Big(\frac{1}{4}\Big)^{-1}=\frac{4}{1}=4$
View full question & answer→Question 161 Mark
Express the following rational numbers with a positive exponent:
$\Big(\frac{5}{4}\Big )^{-3}$
Answer$\Big(\frac{5}{4}\Big )^{-3}=\Big(\frac{5}{4}\Big)^3$
View full question & answer→Question 171 Mark
Express of the following rational numbers with a negative exponent:
$\Big(\frac{1}{4}\Big)^{3}$
Answer$\Big(\frac{1}{4}\Big)^{3}=\Big(\frac{4}{1}\Big)^{-3}=(4)^{-3}$
View full question & answer→Question 181 Mark
Find the values of the following.
$\bigg[\Big(\frac{1}{3}\Big)^{-1}-\Big(\frac{1}{4}\Big)^{-1}\bigg]^{-1}$
Answer$\bigg[\Big(\frac{1}{3}\Big)^{-1}-\Big(\frac{1}{4}\Big)^{-1}\bigg]^{-1}$
$=[(3)^1-(4)^1]=(3-4)^{-1}=(-1)^{-1}$
$=\frac{1}{(-1)^1}=\frac{1}{-1}=-1$
View full question & answer→Question 191 Mark
Write the following numbers in the usual form:
$4.5 \times 10^4$
Answer$4.5 × 10^4=4.5\times10000$
$=45000$
View full question & answer→Question 201 Mark
Express the following rational numbers with a positive exponent:
$\Big(\frac{3}{4}\Big )^{-2}$
Answer$\Big(\frac{3}{4}\Big )^{-2}=\Big(\frac{4}{3}\Big)^2$
View full question & answer→Question 211 Mark
Simplify:$(3^{-1}\times4^{-1})^{-1}\times5^{-1}$
Answer$(3^{-1}\times4^{-1})^{-1}\times5^{-1}$$=\Big(\frac{1}{3}\times\frac{1}{4}\Big)^{-1}\times5^ {-1}$
$=\Big(\frac{1}{12}\Big)^{-1}\times\frac{1}{5}$
$=(12)^{1}\times\frac{1}{5}=\frac{12}{5}$
View full question & answer→Question 221 Mark
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0:$
$\frac{1}{3^{-2}}$
Answer$\frac{1}{3^{-2}}=3^2$
$=3\times3=9$
View full question & answer→Question 231 Mark
Write the following numbers in the usual form:
$5.8 × 10^2$
Answer$5.8 × 10^2$
$5.8\times100=580$
View full question & answer→Question 241 Mark
Express of the following rational numbers with a negative exponent:
$3^5$
Answer$3^5=\Big(\frac{1}{3}\Big)^{-5}$
View full question & answer→Question 251 Mark
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0:$
$\Big(\frac{2}{3}\Big)^{-2}$
Answer$\Big(\frac{2}{3}\Big)^{-2}=\Big(\frac{3}{2}\Big)^2$
$=\frac{3}{2}\times\frac{3}{2}=\frac{9}{4}$
View full question & answer→Question 261 Mark
Express of the following as a rational number in the form $\frac{\text{p}}{\text{q}}:$
$6^{-1}$
Answer$6^{-1}=\frac{1}{6}$
View full question & answer→Question 271 Mark
Simplify:$(3^2+2^2)\times\Big(\frac{1}{2}\Big)^3$
Answer$(3^2+2^2)\times\Big(\frac{1}{2}\Big)^3$
$=(9\div4)\times\frac{1}{8}=13\times\frac{1}{8}$
$=\frac{13}{8}$
View full question & answer→Question 281 Mark
Evaluate:
$5^{-2}$
Answer$5^{-2}$
$=\frac{1}{5^2}=\frac{1}{5\times5}=\frac{1}{25}$
View full question & answer→Question 291 Mark
Simplify:$(2^{-1}+3^{-1})^{-1}$
Answer$(2^{-1}+3^{-1})^{-1}$
$=\Big(\frac{1}{2}+\frac{1}{3}\Big)^{-1}=\Big(\frac{3+2}{6}\Big)^{-1}$
$=\Big(\frac{5}{6}\Big)^{-1}=\frac{6}{5}$
View full question & answer→Question 301 Mark
Find the values of the following.
$\Big(\frac{1}{2}\Big)^{-1}+\Big(\frac{1}{3}\Big)^{-1}+\Big(\frac{1}{4}\Big)^{-1}$
Answer$\Big(\frac{1}{2}\Big)^{-1}+\Big(\frac{1}{3}\Big)^{-1}+\Big(\frac{1}{4}\Big)^{-1}$
$=(2)^1+(3)^1+(4)^1=2+3=9$
View full question & answer→Question 311 Mark
Evaluate:
$\Big( \frac{1}{3}\Big)^{-4}$
Answer$\Big( \frac{1}{3}\Big)^{-4}$
$=\Big( \frac{1}{3}\Big)^{-4}=3\times3\times3\times3=81$
View full question & answer→Question 321 Mark
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0:$
$2^{-3}$
Answer$2^{-3}=\frac{1}{2^3}=\Big(\because\text{a}^{\text{-m}}=\frac{1}{\text{a}^\text{m}}\Big)$
$=\frac{1}{2\times2\times2}=\frac{1}{8}$
View full question & answer→Question 331 Mark
Express of the following as a rational number in the form $\frac{\text{p}}{\text{q}}:$
$(-4)^{-1}\times\Big(\frac{-3}{2}\Big)^{-1}$
Answer$(-4)^{-1}\times\Big(\frac{-3}{2}\Big)^{-1}=\Big(\frac{1}{-4}\Big)^{1}\times\Big(\frac{-2}{3}\Big)^1$
$=\frac{-1}{4}\times\frac{-2}{3}=\frac{1\times1}{2\times3}=\frac{1}{6}$
View full question & answer→Question 341 Mark
Write the following in exponential form:
$\Big(\frac{2}{5}\Big)^{-2}\times\Big(\frac{2}{5}\Big)^{-2}\times\Big(\frac{2}{5}\Big)^{-2}$
Answer$\Big(\frac{2}{5}\Big)^{-2}\times\Big(\frac{2}{5}\Big)^{-2}\times\Big(\frac{2}{5}\Big)^{-2}$
$\Big(\frac{2}{5}\Big)^{-2+(-2)+(-2)}$
$=\Big(\frac{2}{5}\Big)^{-6}$
View full question & answer→Question 351 Mark
Find the values of the following.
$(3^{-1+}4^{-1}+5^{-1})^°$
Answer$(3^{-1+}4^{-1}+5^{-1})^°$$=\Big(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\Big)=1$
View full question & answer→Question 361 Mark
Express of the following rational numbers with a negative exponent:
$\bigg[\Big(\frac{7}{3}\Big)^4\bigg]^{-3}$
Answer$\bigg[\Big(\frac{7}{3}\Big)^4\bigg]^{-3}=\Big(\frac{7}{3}\Big)^{4\times(-3)}=\Big(\frac{7}{3}\Big)^{-12}$
View full question & answer→Question 371 Mark
Simplify:$(3^2-2^2)\times\Big(\frac{2}{3}\Big)^{-3}$
Answer$(3^2-2^2)\times\Big(\frac{2}{3}\Big)^{-3}$
$=(9-4)\times\Big(\frac{3}{2}\Big)^3$
$=5\times\frac{27}{8}=\frac{135}{8}$
View full question & answer→Question 381 Mark
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0:$
$(-4)^{-2}$
Answer$(-4)^{-2}=\frac{1}{(-4)^2}$
$=\frac{1}{(-4)\times(-4)}=\frac{1}{16}$
View full question & answer→Question 391 Mark
Simplify:$(4^{-1}\times3^{-1})^2$
Answer$(4^{-1}\times3^{-1})^2$
$=\Big(\frac{1}{4}\times\frac{1}{3}\Big)^{2}=\Big(\frac{1}{12}\Big)^2$
$=\frac{1}{12}\times\frac{1}{12}=\frac{1}{144}$
View full question & answer→