Question 13 Marks
Evaluate the following :
$(9)^{\frac{5}{2}}-3 .(4)^0-\left(\frac{1}{81}\right)^{-\frac{1}{2}}$
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Evaluate the following :
$(\sqrt{32}-\sqrt{5})^{\frac{1}{3}}(\sqrt{32}+\sqrt{5})^{\frac{1}{3}}$
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Evaluate the following :
$\left\{\frac{(27)^{-3}}{9^{-3}}\right\}^{\frac{1}{3}}$
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Evaluate the following :
$\left\{\frac{(27)^{-3}}{9^{-3}}\right\}^{\frac{1}{3}}$
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Evaluate the following :
$(27)^{\frac{4}{3}}+(32)^{0.8}+(0 \cdot 8)^{-1}+(0 \cdot 8)^0$
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Evaluate the following :
$\left(\frac{64}{125}\right)^{-\frac{2}{3}} \div \frac{1}{\left(\frac{256}{625}\right)^{\frac{1}{4}}}+\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)^0$
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Evaluate the following :
$\left(\frac{16}{81}\right)^{-\frac{3}{4}} \times\left(\frac{49}{9}\right)^{\frac{3}{2}}+\left(\frac{343}{216}\right)^{\frac{2}{3}}$
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Evaluate the following :
$\quad(81)^{\frac{3}{4}}-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+(8)^{\frac{1}{3}} \cdot\left(\frac{1}{2}\right)^{-1}$.$(2)^0$
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Evaluate the following :
$\left[(64)^{2 / 3} \times 2^{-2} \div 7^0\right]^{-\frac{1}{2}}$
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Evaluate the following :
$\left(\frac{81}{16}\right)^{-\frac{3}{4}} \times\left[\left(\frac{25}{9}\right)^{-\frac{3}{2}} \div\left(\frac{5}{2}\right)^{-3}\right]$
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Evaluate the following :
$\sqrt{\frac{1}{4}}+(0.01)^{\frac{-1}{2}}-(27)^{2 / 3} \times 3^0$
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Evaluate the following :
$\left(\frac{1}{4}\right)^{-2}-3 \times 8^{\frac{2}{3}} \times 5^0+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$
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Prove that : $\frac{1}{1+x^{b-a}+x^{c-a}}+\frac{1}{1+x^{a-b}+x^{c-b}}+\frac{1}{1+x^{b-c}+x^{a-c}}=1$.
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Prove that : $\frac{a^{-1}}{\left(a^{-1}+b^{-1}\right)}+\frac{a^{-1}}{\left(a^{-1}-b^{-1}\right)}=\frac{2 b^2}{\left(b^2-a^2\right)}$.
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Prove that : $\left(\frac{x^a}{x^b}\right)^{(a+b-c)} \cdot\left(\frac{x^b}{x^c}\right)^{(b+c-a)} \cdot\left(\frac{x^c}{x^a}\right)^{c+a-b}=1$.
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Prove that : $\left(\frac{x^a}{x^b}\right)^{\frac{1}{b b}} \cdot\left(\frac{x^b}{x^c}\right)^{\frac{1}{b e}} \cdot\left(\frac{x^c}{x^a}\right)^{\frac{1}{b e}}=1$.
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Prove that : $\left(\frac{x^a}{x^b}\right)^{(a+b)} \cdot\left(\frac{x^b}{x^c}\right)^{(b+c)} \cdot\left(\frac{x^c}{x^a}\right)^{(c+a)}=1$.
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If $2^x=3^y=6^{-z}$, show that : $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$.
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If $2^x=3^y=12^z$, show that $: \frac{1}{z}=\frac{1}{y}+\frac{2}{x}$.
[ Hint. Let $2^x=3^y=12^z=k$. Then, $2=k^{\frac{1}{x}}, 3=k^{\frac{1}{y}}$ and $12=k^{\frac{1}{z}}$.
Now, $\left.12=2^2 \times 3 \Rightarrow k^{\frac{1}{2}}=\left(k^{\frac{1}{x}}\right)^2 \times\left(k^{\frac{1}{y}}\right) \Rightarrow k^{\frac{1}{2}}=k^{\left(\frac{2}{x}+\frac{1}{y}\right)}\right]$
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Solve for n:
$\left(3^n \times 9^{n+1}\right) \div\left(3^{n-1} \times 27^{n-1}\right)=81$
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Evaluate the following:
$(9)^{\frac{5}{2}}-3 .(4)^0-\left(\frac{1}{81}\right)^{-\frac{1}{2}}$
View full question & answer→Question 223 Marks
Evaluate the following:
$(\sqrt{32}-\sqrt{5})^{\frac{1}{3}}(\sqrt{32}+\sqrt{5})^{\frac{1}{3}}$
View full question & answer→Question 233 Marks
Evaluate the following:
$\left\{\frac{(27)^{-3}}{9^{-3}}\right\}^{\frac{1}{3}}$
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Evaluate the following:
$(27)^{\frac{4}{3}}+(32)^{0.8}+(0 \cdot 8)^{-1}+(0 \cdot 8)^0$
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Evaluate the following:
$\frac{(32)^{2 / 5} \times(4)^{-\frac{1}{2}} \times(8)^{\frac{1}{3}}}{2^{-2} \div(64)^{-1 / 3}}$
View full question & answer→Question 263 Marks
Evaluate the following:
$\left(\frac{64}{125}\right)^{-\frac{2}{3}} \div \frac{1}{\left(\frac{256}{625}\right)^{\frac{1}{4}}}+\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)^0$
View full question & answer→Question 273 Marks
Evaluate the following:
$\left(\frac{16}{81}\right)^{-\frac{3}{4}} \times\left(\frac{49}{9}\right)^{\frac{3}{2}} \div\left(\frac{343}{216}\right)^{\frac{2}{3}}$
View full question & answer→Question 283 Marks
Evaluate the following:
$(81)^{\frac{3}{4}}-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+(8)^{\frac{1}{3}} \cdot\left(\frac{1}{2}\right)^{-1} \cdot(2)^0$
View full question & answer→Question 293 Marks
Evaluate the following:
$\left[(64)^{2 / 3} \times 2^{-2} \div 7^0\right]^{-\frac{1}{2}}$
View full question & answer→Question 303 Marks
Evaluate the following:
$\left(\frac{81}{16}\right)^{-\frac{3}{4}} \times\left[\left(\frac{25}{9}\right)^{-\frac{3}{2}} \div\left(\frac{5}{2}\right)^{-3}\right]$
View full question & answer→Question 313 Marks
Evaluate the following:
$\sqrt{\frac{1}{4}}+(0.01)^{\frac{-1}{2}}-(27)^{2 / 3} \times 3^0$
View full question & answer→Question 323 Marks
Evaluate the following:
$\left(\frac{1}{4}\right)^{-2}-3 \times 8^{\frac{2}{3}} \times 5^0+\left(\frac{9}{16}\right)^{-\frac{1}{2}}$
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