Educational

√64 ÷ ∛64 Simplification 🎥 Watch Video Solution Q. \( \sqrt{64} \div \sqrt[3]{64} \) ✏️ Solution \( = 64^{1/2} \div 64^{1/3} \) \( = 64^{\left(\frac{1}{2} – \frac{1}{3}\right)} \) \( = 64^{\frac{1}{6}} \) \( = (2^6)^{\frac{1}{6}} \) \( = 2 \) \( \boxed{2} \) Next Question / Full Exercise

7th Root x ÷ 8th Root x 🎥 Watch Video Solution Q. \( \sqrt[7]{x} \div \sqrt[8]{x} \) ✏️ Solution \( = x^{1/7} \div x^{1/8} \) \( = x^{\left(\frac{1}{7} – \frac{1}{8}\right)} \) \( = x^{\frac{8-7}{56}} \) \( = x^{\frac{1}{56}} \) \( = \sqrt[56]{x} \) \( \boxed{\sqrt[56]{x}} \) Next Question / Full Exercise

Product of √x and ∛x 🎥 Watch Video Solution Q. The product of \( \sqrt{x} \) and \( \sqrt[3]{x} \), is (a) \( \sqrt[3]{\sqrt{x}} \) (b) \( \sqrt[6]{x^5} \) (c) \( \sqrt[5]{x^6} \) (d) \( \sqrt[6]{x} \) ✏️ Solution \( \sqrt{x} \times \sqrt[3]{x} \) \( = x^{1/2} \times x^{1/3} \) \( = x^{\left(\frac{1}{2}+\frac{1}{3}\right)} \) \(

MCQ Exponent Evaluation 🎥 Watch Video Solution Q. \( x – y^{x-y} \), when \( x = 2, y = -2 \) (a) 18    (b) -18    (c) 14    (d) -14 ✏️ Solution \( x – y^{x-y} \) \( = 2 – (-2)^{2-(-2)} \) \( = 2 – (-2)^4 \) \( = 2

256^0.16 × 256^0.09 Simplification 🎥 Watch Video Solution Q. \( (256)^{0.16} \times (256)^{0.09} \) ✏️ Solution \( = 256^{0.16+0.09} \) \( = 256^{0.25} \) \( = 256^{\frac{1}{4}} \) \( = (2^8)^{\frac{1}{4}} \) \( = 2^2 \) \( = 4 \) \( \boxed{4} \) Next Question / Full Exercise

MCQ Exponent Simplification 🎥 Watch Video Solution Q. \( \{2 – 3(2 – 3)^3\}^3 \) (a) 5    (b) 125    (c) \( \frac{1}{5} \)    (d) -125 ✏️ Solution \( = \{2 – 3(-1)^3\}^3 \) \( = \{2 – 3(-1)\}^3 \) \( = (2 + 3)^3 \) \( = 5^3 \) \( = 125

4th Root of (81^-2) Simplification 🎥 Watch Video Solution Q. \( \sqrt[4]{(81)^{-2}} \) ✏️ Solution \( = (81^{-2})^{\frac{1}{4}} \) \( = 81^{-\frac{2}{4}} \) \( = 81^{-\frac{1}{2}} \) \( = (9^2)^{-\frac{1}{2}} \) \( = 9^{-1} \) \( = \frac{1}{9} \) \( \boxed{\frac{1}{9}} \) Next Question / Full Exercise

Product of Roots Simplification 🎥 Watch Video Solution Q. \( \sqrt[3]{2} \times \sqrt[4]{2} \times \sqrt[12]{32} \) ✏️ Solution \( = 2^{1/3} \times 2^{1/4} \times (2^5)^{1/12} \) \( = 2^{1/3} \times 2^{1/4} \times 2^{5/12} \) \( = 2^{\left(\frac{1}{3}+\frac{1}{4}+\frac{5}{12}\right)} \) \( = 2^{\left(\frac{4+3+5}{12}\right)} \) \( = 2^{1} \) \( = 2 \) \( \boxed{2} \) Next Question

Nested Root Simplification 🎥 Watch Video Solution Q. \( \sqrt[4]{\sqrt[3]{\sqrt{2^2}}} \) ✏️ Solution \( = \sqrt[4]{\sqrt[3]{2}} \) \( = \sqrt[4]{2^{1/3}} \) \( = 2^{\frac{1}{3} \times \frac{1}{4}} \) \( = 2^{1/12} \) \( \boxed{2^{1/12}} \) Next Question / Full Exercise

Find x² − y² in Exponent Equation 🎥 Watch Video Solution Q. \( 6^{x-y} = 36,\quad 3^{x+y} = 729 \) ✏️ Solution \( 36 = 6^2 \) \( 6^{x-y} = 6^2 \Rightarrow x-y = 2 \) \( 729 = 3^6 \) \( 3^{x+y} = 3^6 \Rightarrow x+y = 6 \) \( x^2 – y^2 =