Surds and Indices Questions Answers Online Quiz Test
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1. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}
- 1012
- 1024
- 1048
- 525
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2. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}
- 2
- 4
- \begin{aligned} \sqrt{2} \end{aligned}
- 8
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3. Find the value of,
\begin{aligned}
\frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}}
\end{aligned}- 100
- 101
- 102
- 103
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4. Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}- 10
- 100
- 1000
- 10000
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5. \begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}
- 10
- 100
- 1000
- 10000
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6. If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m-1)^{n + 1} \end{aligned} is- 1
- 10
- 100
- 1000
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7. Evaluate \begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}
- 2
- 4
- 8
- 16
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8. \begin{align}
\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?}
\end{align}- 1.5
- 4.5
- 7.5
- 9.5
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9. \begin{aligned}
\text{If }x = \left(8 + 3\sqrt{7}\right),\text{ what is the value of }\\\left(\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)?
\end{aligned}
- \begin{aligned} \sqrt{13} \end{aligned}
- \begin{aligned} \sqrt{14} \end{aligned}
- \begin{aligned} \sqrt{15} \end{aligned}
- \begin{aligned} \sqrt{16} \end{aligned}
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10. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2
\end{aligned}- 25
- 28
- 36
- 44
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11. \begin{aligned}
\text{If }2x = \sqrt[3]{32}, \text{ then x is equal to}
\end{aligned}
- \begin{aligned} \frac{5}{2} \end{aligned}
- \begin{aligned} \frac{2}{5} \end{aligned}
- \begin{aligned} \frac{3}{5} \end{aligned}
- \begin{aligned} \frac{5}{3} \end{aligned}
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12. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}- 1
- 2
- 3
- 4
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13. \begin{aligned}
\frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ?
\end{aligned}- 1
- 2
- 3
- 4
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14. \begin{aligned}
\text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\
\text{ then find the value of x }
\end{aligned}- 1
- 2
- 3
- 4
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15. \begin{aligned}
\text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2}
\end{aligned}- 7776
- 7782
- 1296
- 1290
-
16. \begin{aligned}
\left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^?
\end{aligned}- 9.7
- 11.5
- 12
- 13