Question Detail

$\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}$

Answer: Option A

Explanation:

$\begin{aligned} = \frac{1}{\left( 1 + \frac{a^n}{a^m} \right)} + \frac{1}{\left( 1 + \frac{a^m}{a^n} \right)} \\ = \frac{a^m}{(a^m+a^n)} + \frac{a^n}{(a^m+a^n)} \\ = \frac{(a^m+a^n)}{(a^m+a^n)} = 1 \end{aligned}$

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

10
100
1000
10000

Answer: Option C

Explanation:

$\begin{aligned} = \frac{(10^3)^7}{(10)^{18}} \end{aligned}$

$\begin{aligned} = \frac{(10)^{21}}{(10)^{18}} = 10^3 = 1000 \end{aligned}$

3. Evaluate $\begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}$

Answer: Option B

Explanation:

$\begin{aligned} = 256^{0.16+0.09} = 256^{0.25} = 256^{\frac{25}{100}} \end{aligned}$

$\begin{aligned} = 256^{\frac{1}{4}}= (4^4)^{\frac{1}{4}} \end{aligned}$

$\begin{aligned} =(4)^{4 \times \frac{1}{4}} = 4 \end{aligned}$

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

7776
7782
1296
1290

Answer: Option C

Explanation:

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

5. Find the value of,
$\begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}$

Answer: Option C

Question Detail

$\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}$

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

3. Evaluate $\begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}$

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

5. Find the value of,
$\begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}$

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Question Detail

11+a(n−m)+11+a(m−n)=?\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}

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

2. (1000)7÷(10)18=?\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}

3. Evaluate 2560.16×(256)0.09\begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}

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

5. Find the value of, 1216−23+1256−34+132−15\begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}

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$\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}$

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

3. Evaluate $\begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}$

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

5. Find the value of,
$\begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}$