Question Detail

$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^? \end{aligned}$

9.7
11.5
12
13

Answer: Option D

Explanation:

Lets assume,

$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\ \text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\ => \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\ => 5^x = 5^{15 + 2.5 - 4.5} \\ => 5^x = 5^{13} \\ \text{Hence, } x = 13 \end{aligned}$

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

2
4
$\begin{aligned} \sqrt{2} \end{aligned}$
8

Answer: Option C

Explanation:

$\begin{aligned} = ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})} \end{aligned}$

$\begin{aligned} = (8)^{\frac{1}{6}} \end{aligned}$

$\begin{aligned} = (2)^{3(\frac{1}{6})} \end{aligned}$

$\begin{aligned} = (2)^{\frac{1}{2}} \end{aligned}$

2. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

$\begin{aligned} \frac{5}{2} \end{aligned}$
$\begin{aligned} \frac{2}{5} \end{aligned}$
$\begin{aligned} \frac{3}{5} \end{aligned}$
$\begin{aligned} \frac{5}{3} \end{aligned}$

Answer: Option D

Explanation:

$\begin{aligned} = (32)^{\frac{1}{3}}\\ = (2^5)^{\frac{1}{3}}\\ = 2^{\frac{5}{3}}\\ => x= \frac{5}{3} \end{aligned}$

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

Answer: Option A

Explanation:

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

4. 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

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

Answer: Option B

Explanation:

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

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

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

Question Detail

$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^? \end{aligned}$

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

2. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

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

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

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

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Question Detail

(25)7.5×(5)2.5÷(125)1.5=5?\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^? \end{aligned}

1. √813\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}

2. If 2x=3√32, then x is equal to\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}

3. 11+a(n−m)+11+a(m−n)=?\begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}

4. 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}

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

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$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^? \end{aligned}$

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

2. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

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

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

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