# Surds and Indices Questions Answers

• #### 1. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}

1. 1012
2. 1024
3. 1048
4. 525

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}

1. 2
2. 4
3. \begin{aligned} \sqrt{2} \end{aligned}
4. 8

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}

1. 100
2. 101
3. 102
4. 103

Explanation:

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

1. 10
2. 100
3. 1000
4. 10000

Explanation:

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

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

1. 10
2. 100
3. 1000
4. 10000

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} (m-1)^{n + 1} \end{aligned} is

1. 1
2. 10
3. 100
4. 1000

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}

• #### 7. Evaluate \begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}

1. 2
2. 4
3. 8
4. 16

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 5 years ago

HEY QNS COPIED FROM QUANTITATIVE APP. S.CHAND

x is 7÷16

• #### asuquo rosy 6 years ago

If x = root3 - root2 / root3 + root 2, y = root3 + root2 / root3 - root2. Find the value of 3x^2 - 5x + 3y^2.

• #### dian 7 years ago

Same questions seen everywhere

• #### Savi 7 years ago

Good questions