Question Detail

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}
Similar Questions :

1. 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}

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}

  • 100
  • 101
  • 102
  • 103

Answer: Option C

3. \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}

4. \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

Answer: Option D

Explanation:

\begin{aligned}3^{x-y} = 27 = 3^3 <=> x-y = 3 \text{... (i)}\\
3^{x+y} = 243 = 3^5 <=> x+y = 5 \text{... (ii)} \\

\text{ adding (i) and (ii)}
=> 2x = 8 \\
=> x = 4
\end{aligned}

5. \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}

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