Question Detail

Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}

1012
1024
1048
525

Answer: Option B

Explanation:

\begin{aligned}
= (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024
\end{aligned}

1. \begin{aligned}
\text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\
\text{ then find the value of x }
\end{aligned}

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}

2. \begin{aligned}
\text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2}
\end{aligned}

7776
7782
1296
1290

Answer: Option C

Explanation:

\begin{aligned}
6^{m-2}\\ = \dfrac{6^m}{6^2}\\ = \dfrac{46656}{6^2}\\ = \dfrac{46656}{36} = 1296
\end{aligned}

3. \begin{align}
\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?}
\end{align}

Answer: Option B

Explanation:

\begin{align}&\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}\\\\
&\Rightarrow \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{a}{b}\right)^{-(x-7)}\\\\
&\Rightarrow x - 2 = -(x - 7)\\\\
&\Rightarrow x - 2 = -x + 7\\\\
&\Rightarrow x-2 = -x + 7\\\\
&\Rightarrow 2x = 9\\\\
&\Rightarrow x = \dfrac{9}{2} = 4.5
\end{align}

4. 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}

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

Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}

1. \begin{aligned} \text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\ \text{ then find the value of x } \end{aligned}

2. \begin{aligned} \text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2} \end{aligned}

3. \begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}

4. 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

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

1. \begin{aligned}
\text{If } 3^{x-y} = 27 \text{ and } 3^{x+y} = 243, \\
\text{ then find the value of x }
\end{aligned}

2. \begin{aligned}
\text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2}
\end{aligned}

3. \begin{align}
\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?}
\end{align}

4. 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