Educational

Find x in Exponent Equation 🎥 Watch Video Solution Q. If \( \frac{x}{x^{1.5}} = 8x^{-1} \) and \( x > 0 \), find \( x \) (a) \( \frac{\sqrt{2}}{4} \)    (b) \( 2\sqrt{2} \)    (c) 4    (d) 64 ✏️ Solution \( \frac{x}{x^{1.5}} = x^{1 – 1.5} \) \( = x^{-0.5} \) \(

Find x^3 🎥 Watch Video Solution Q. If \( x^2 = 2 \), find \( x^3 \) (a) \( \sqrt{2} \)    (b) \( 2\sqrt{2} \)    (c) \( 3\sqrt{2} \)    (d) 4 ✏️ Solution \( x^2 = 2 \) \( x = \sqrt{2} \) (since x is positive) \( x^3 = x \cdot

Find x in Exponent Equation 🎥 Watch Video Solution Q. If \( 9^{x+2} = 240 + 9^x \), find \( x \) (a) 0.5    (b) 0.2    (c) 0.4    (d) 0.1 ✏️ Solution \( 9^{x+2} = 9^x \cdot 9^2 \) \( = 81 \cdot 9^x \) \( 81 \cdot 9^x = 240 +

Find 10^-y 🎥 Watch Video Solution Q. If \( 10^{2y} = 25 \), find \( 10^{-y} \) (a) \( -\frac{1}{5} \)    (b) \( \frac{1}{50} \)    (c) \( \frac{1}{625} \)    (d) \( \frac{1}{5} \) ✏️ Solution \( 10^{2y} = 25 \) \( (10^y)^2 = 25 \) \( 10^y = 5 \) \( 10^{-y}

Exponent Simplification 🎥 Watch Video Solution Q. \( (256)^{0.16} \times (256)^{0.09} \) (a) 4    (b) 16    (c) 64    (d) 256.25 ✏️ Solution \( = 256^{0.16+0.09} \) \( = 256^{0.25} \) \( = 256^{\frac{1}{4}} \) \( = (2^8)^{\frac{1}{4}} \) \( = 2^2 \) \( = 4 \) Correct Option: (a) 4 \( \boxed{4}

Decimal Exponent Simplification 🎥 Watch Video Solution Q. \( (0.00243)^{\frac{3}{5}} + (0.0256)^{\frac{3}{4}} \) (a) 0.083    (b) 0.073    (c) 0.081    (d) 0.091 ✏️ Solution \( 0.00243 = (0.3)^5 \) \( (0.00243)^{3/5} = (0.3)^3 = 0.027 \) \( 0.0256 = (0.4)^4 \) \( (0.0256)^{3/4} = (0.4)^3 = 0.064 \) \( = 0.027 + 0.064

Find m in Exponent Equation 🎥 Watch Video Solution Q. \( \left[\{(1/7^2)^{-2}\}^{-\frac{1}{3}}\right]^{\frac{1}{4}} = 7^m \) (a) \( -\frac{1}{3} \)    (b) \( \frac{1}{4} \)    (c) -3    (d) 2 ✏️ Solution \( \frac{1}{7^2} = 7^{-2} \) \( (7^{-2})^{-2} = 7^{4} \) \( (7^{4})^{-1/3} = 7^{-4/3} \) \( (7^{-4/3})^{1/4} = 7^{-4/12} \) \( = 7^{-1/3}

Exponent Evaluation 🎥 Watch Video Solution Q. If \( x = 2, y = 4 \), find \( \left(\frac{x}{y}\right)^{x-y} + \left(\frac{y}{x}\right)^{y-x} \) (a) 4    (b) 8    (c) 12    (d) 2 ✏️ Solution \( \left(\frac{2}{4}\right)^{2-4} + \left(\frac{4}{2}\right)^{4-2} \) \( = \left(\frac{1}{2}\right)^{-2} + (2)^2 \) \( = 2^2 + 4 \) \( = 4

Nested Root Simplification 🎥 Watch Video Solution Q. \( \left(\sqrt[m]{\sqrt[n]{a}}\right)^{mn} \) (a) \( a^{mn} \)    (b) \( a \)    (c) \( a^{m/n} \)    (d) 1 ✏️ Solution \( \sqrt[n]{a} = a^{1/n} \) \( \sqrt[m]{\sqrt[n]{a}} = (a^{1/n})^{1/m} \) \( = a^{1/(mn)} \) \( \left(a^{1/(mn)}\right)^{mn} \) \( = a \) Correct Option: (b) \(

5th Root Simplification 🎥 Watch Video Solution Q. \( \sqrt[5]{3125a^{10}b^5c^{10}} \) (a) \( 5a^2bc^2 \)    (b) \( 25ab^2c \)    (c) \( 5a^3bc^3 \)    (d) \( 125a^2bc^2 \) ✏️ Solution \( 3125 = 5^5 \) \( = \sqrt[5]{5^5 \cdot a^{10} \cdot b^5 \cdot c^{10}} \) \( = 5 \cdot a^{10/5} \cdot b^{5/5} \cdot