Question Detail \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned} 25283644 Answer: Option C Similar Questions : 1. 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} 100101102103 Answer: Option C 2. \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} 1.54.57.59.5 Answer: Option BExplanation:\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} 3. Find the value of \begin{aligned} (10)^{150} \div (10)^{146} \end{aligned} 10100100010000 Answer: Option DExplanation:\begin{aligned} = \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000 \end{aligned} 4. \begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned} 24\begin{aligned} \sqrt{2} \end{aligned}8 Answer: Option CExplanation:\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} 5. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned} 101210241048525 Answer: Option BExplanation:\begin{aligned} = (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024 \end{aligned} Read more from - Surds and Indices Questions Answers