Question Detail

Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}

10
100
1000
10000

Answer: Option D

Explanation:

\begin{aligned}
= \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000
\end{aligned}

1. \begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}

10
100
1000
10000

Answer: Option C

Explanation:

\begin{aligned}
= \frac{(10^3)^7}{(10)^{18}}
\end{aligned}

\begin{aligned}
= \frac{(10)^{21}}{(10)^{18}} = 10^3 = 1000
\end{aligned}

2. 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}

Answer: Option C

3. 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

Answer: Option D

Explanation:

We know that \begin{aligned} (11)^2 = 121
\end{aligned}
So, putting values in said equation we get,
\begin{aligned} (11-1)^{2 + 1} = (10)^3 = 1000 \end{aligned}

4. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}

Answer: Option B

Explanation:

Clue:

\begin{aligned}
(\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \
\end{aligned}
Now put the value of x to calculate the answer :)

5. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}

2
4
\begin{aligned} \sqrt{2} \end{aligned}
8

Answer: Option C

Explanation:

\begin{aligned}
= ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})}
\end{aligned}

\begin{aligned}
= (8)^{\frac{1}{6}}
\end{aligned}

\begin{aligned}
= (2)^{3(\frac{1}{6})}
\end{aligned}

\begin{aligned}
= (2)^{\frac{1}{2}}
\end{aligned}

Question Detail

Find the value of \begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}

1. \begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}

2. 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}

3. 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

4. \begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}

5. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}

Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}

2. 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}

3. 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

4. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}