Surds and Indices Questions Answers

1. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}
 1012
 1024
 1048
 525
Answer And Explanation
Answer: Option B
Explanation:
\begin{aligned}
= (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024
\end{aligned} 
2. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}
 2
 4
 \begin{aligned} \sqrt{2} \end{aligned}
 8
Answer And Explanation
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} 
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
Answer And Explanation
Answer: Option C
Explanation:

4. Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned} 10
 100
 1000
 10000
Answer And Explanation
Answer: Option D
Explanation:
\begin{aligned}
= \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000
\end{aligned} 
5. \begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}
 10
 100
 1000
 10000
Answer And Explanation
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} 
6. If m and n are whole numbers such that
\begin{aligned} m^n=121 \end{aligned}
, the value of \begin{aligned} (m1)^{n + 1} \end{aligned} is 1
 10
 100
 1000
Answer And Explanation
Answer: Option D
Explanation:
We know that \begin{aligned} (11)^2 = 121
\end{aligned}
So, putting values in said equation we get,
\begin{aligned} (111)^{2 + 1} = (10)^3 = 1000 \end{aligned} 
7. Evaluate \begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}
 2
 4
 8
 16
Answer And Explanation
Answer: Option B
Explanation:
\begin{aligned}
= 256^{0.16+0.09} = 256^{0.25} = 256^{\frac{25}{100}}
\end{aligned}
\begin{aligned}
= 256^{\frac{1}{4}}= (4^4)^{\frac{1}{4}}
\end{aligned}
\begin{aligned}
=(4)^{4 \times \frac{1}{4}} = 4
\end{aligned}

SHAN 3 years ago
HEY QNS COPIED FROM QUANTITATIVE APP. S.CHAND

kumar 3 years ago
i want to know the answer of 2^x=4^y=8^z and (1/2x+1/4y+1/6z)=24/7

asuquo rosy 4 years ago
If x = root3  root2 / root3 + root 2, y = root3 + root2 / root3  root2. Find the value of 3x^2  5x + 3y^2.

dian 4 years ago
Same questions seen everywhere

Savi 5 years ago
Good questions