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Question Detail
\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}
Answer: Option D
Explanation:
\begin{aligned}
= (32)^{\frac{1}{3}}\\
= (2^5)^{\frac{1}{3}}\\
= 2^{\frac{5}{3}}\\
=> x= \frac{5}{3}
\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. Evaluate \begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}
- 2
- 4
- 8
- 16
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}
3. \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
Answer: Option D
Explanation:
Lets assume,
\begin{aligned}
\left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\
\text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\
=> \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\
=> 5^x = 5^{15 + 2.5 - 4.5} \\
=> 5^x = 5^{13} \\
\text{Hence, } x = 13
\end{aligned}
4. \begin{aligned}
\frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ?
\end{aligned}
- 1
- 2
- 3
- 4
Answer: Option A
Explanation:
\begin{aligned}
= \frac{1}{\left( 1 + \frac{a^n}{a^m} \right)} +
\frac{1}{\left( 1 + \frac{a^m}{a^n} \right)} \\
= \frac{a^m}{(a^m+a^n)} + \frac{a^n}{(a^m+a^n)} \\
= \frac{(a^m+a^n)}{(a^m+a^n)} = 1
\end{aligned}
5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2
\end{aligned}
- 25
- 28
- 36
- 44
Answer: Option C
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