Ravi Kant Kumar

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 […]

Exponent Expression Simplification 🎥 Watch Video Solution Q. \( \left\{8^{-\frac{4}{3}} \div 2^{-2}\right\}^{\frac{1}{2}} \) (a) \( \frac{1}{2} \)    (b) 2    (c) \( \frac{1}{4} \)    (d) 4 ✏️ Solution \( 8 = 2^3 \) \( 8^{-\frac{4}{3}} = (2^3)^{-\frac{4}{3}} \) \( = 2^{-4} \) \( = \frac{1}{16} \) \( \frac{1}{16} \div 2^{-2} = \frac{1}{16} \div

Find x in Exponent Equation 🎥 Watch Video Solution Q. \( \left(\frac{2}{3}\right)^x \left(\frac{3}{2}\right)^{2x} = \frac{81}{16} \) (a) 2    (b) 3    (c) 4    (d) 1 ✏️ Solution \( \left(\frac{3}{2}\right)^{2x} = \left(\frac{2}{3}\right)^{-2x} \) \( \left(\frac{2}{3}\right)^x \cdot \left(\frac{2}{3}\right)^{-2x} = \frac{81}{16} \) \( \left(\frac{2}{3}\right)^{-x} = \frac{81}{16} \) \( \left(\frac{3}{2}\right)^x = \frac{81}{16} \) \( \frac{81}{16} = \frac{3^4}{2^4}

Exponent MCQ Simplification 🎥 Watch Video Solution Q. \( \sqrt{a^{-1}b} \times \sqrt{b^{-1}c} \times \sqrt{c^{-1}a} \) (a) 1    (b) abc    (c) \( \sqrt{abc} \)    (d) \( \frac{1}{abc} \) ✏️ Solution \( = \sqrt{\frac{b}{a}} \times \sqrt{\frac{c}{b}} \times \sqrt{\frac{a}{c}} \) \( = \sqrt{\frac{b}{a} \cdot \frac{c}{b} \cdot \frac{a}{c}} \) \( = \sqrt{1} \) \( = 1

Exponent MCQ Simplification 🎥 Watch Video Solution Q. Which one is NOT equal to \( \left(\frac{100}{9}\right)^{-\frac{3}{2}} \) ? (a) \( \left(\frac{9}{100}\right)^{\frac{3}{2}} \) (b) \( \frac{1}{\left(\frac{100}{9}\right)^{\frac{3}{2}}} \) (c) \( \frac{3}{10} \times \frac{3}{10} \times \frac{3}{10} \) (d) \( \sqrt{\frac{100}{9} \times \frac{100}{9} \times \frac{100}{9}} \) ✏️ Solution \( \left(\frac{100}{9}\right)^{-\frac{3}{2}} = \left(\frac{9}{100}\right)^{\frac{3}{2}} \) \( = \left(\frac{3}{10}\right)^3 \) \( =

Exponent MCQ Simplification 🎥 Watch Video Solution Q. Which one is NOT equal to \( (\sqrt[3]{8})^{-1/2} \) ? (a) \( (\sqrt[3]{2})^{-1/2} \) (b) \( 8^{-1/6} \) (c) \( \frac{1}{(\sqrt[3]{8})^{1/2}} \) (d) \( \frac{1}{\sqrt{2}} \) ✏️ Solution \( \sqrt[3]{8} = 2 \) \( (\sqrt[3]{8})^{-1/2} = 2^{-1/2} \) \( = \frac{1}{\sqrt{2}} \) (a) \( (\sqrt[3]{2})^{-1/2} = 2^{-1/6}

(-1/27)^(-2/3) Simplification 🎥 Watch Video Solution Q. \( \left(-\frac{1}{27}\right)^{-\frac{2}{3}} \) ✏️ Solution \( = \left[\left(-\frac{1}{27}\right)^{\frac{1}{3}}\right]^{-2} \) \( = \left(-\frac{1}{3}\right)^{-2} \) \( = (-3)^2 \) \( = 9 \) \( \boxed{9} \) Next Question / Full Exercise

Find x^(1/3) + x^0 🎥 Watch Video Solution Q. If \( x^{-2} = 64 \), find \( x^{\frac{1}{3}} + x^0 \) (a) 2    (b) 3    (c) \( \frac{3}{2} \)    (d) \( \frac{2}{3} \) ✏️ Solution \( x^{-2} = 64 \) \( \frac{1}{x^2} = 64 \) \( x^2 = \frac{1}{64} \) \( x

Find 3^x 🎥 Watch Video Solution Q. If \( (2^3)^2 = 4^x \), find \( 3^x \) (a) 3    (b) 6    (c) 9    (d) 27 ✏️ Solution \( (2^3)^2 = 2^6 \) \( 4^x = (2^2)^x = 2^{2x} \) \( 2^6 = 2^{2x} \) \( 6 = 2x \) \( x =

Find 3^(2x+1) 🎥 Watch Video Solution Q. If \( 8^{x+1} = 64 \), find \( 3^{2x+1} \) (a) 1    (b) 3    (c) 9    (d) 27 ✏️ Solution \( 8 = 2^3,\quad 64 = 2^6 \) \( (2^3)^{x+1} = 2^6 \) \( 2^{3(x+1)} = 2^6 \) \( 3(x+1) = 6 \) \( x+1