Ravi Kant Kumar

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 = […]

Find x and y in Exponent Equation 🎥 Watch Video Solution Q. \( \frac{1}{243^x} = 729^y = 3^3 \) ✏️ Solution \( 243 = 3^5,\quad 729 = 3^6 \) \( \frac{1}{243^x} = (3^5)^{-x} = 3^{-5x} \) \( 729^y = (3^6)^y = 3^{6y} \) \( 3^{-5x} = 3^3 \Rightarrow -5x = 3 \) \( x =

Exponent Expression Simplification 🎥 Watch Video Solution Q. \( \left[\frac{a^{3-7a}\cdot a^{6-2a}}{a^{2a}\cdot a^{9-2a}}\right]^{\frac{1}{9}} \) ✏️ Solution \( = \left[\frac{a^{(3-7a)+(6-2a)}}{a^{2a+(9-2a)}}\right]^{\frac{1}{9}} \) \( = \left[\frac{a^{9-9a}}{a^{9}}\right]^{\frac{1}{9}} \) \( = \left[a^{-9a}\right]^{\frac{1}{9}} \) \( = a^{-a} \) \( \boxed{a^{-a}} \) Next Question / Full Exercise

Find (12n+3)^(1/3) 🎥 Watch Video Solution Q. \( 5^{n+2} = 625 \), find \( (12n+3)^{\frac{1}{3}} \) ✏️ Solution \( 625 = 5^4 \) \( 5^{n+2} = 5^4 \) \( n+2 = 4 \) \( n = 2 \) \( (12n+3)^{\frac{1}{3}} = (12\times2 + 3)^{\frac{1}{3}} \) \( = (24 + 3)^{\frac{1}{3}} \) \( = 27^{\frac{1}{3}} \)

Find x in Exponent Expression 🎥 Watch Video Solution Q. \( \frac{(p+\frac{1}{q})^{p-q}(p-\frac{1}{q})^{p+q}}{(q+\frac{1}{p})^{p-q}(q-\frac{1}{p})^{p+q}} = \left(\frac{p}{q}\right)^x \) ✏️ Solution \( = \frac{\left(\frac{pq+1}{q}\right)^{p-q}\left(\frac{pq-1}{q}\right)^{p+q}}{\left(\frac{pq+1}{p}\right)^{p-q}\left(\frac{pq-1}{p}\right)^{p+q}} \) \( = \frac{(pq+1)^{p-q}(pq-1)^{p+q}}{q^{p-q}q^{p+q}} \div \frac{(pq+1)^{p-q}(pq-1)^{p+q}}{p^{p-q}p^{p+q}} \) \( = \frac{1}{q^{2p}} \div \frac{1}{p^{2p}} \) \( = \frac{p^{2p}}{q^{2p}} \) \( = \left(\frac{p}{q}\right)^{2p} \) \( x = 2p \) \( \boxed{2p} \) Next Question / Full Exercise

((a/b)^(√99−√97))^(√99+√97) Solution 🎥 Watch Video Solution Q. Simplify \( \left\{\left(\frac{a}{b}\right)^{\sqrt{99}-\sqrt{97}}\right\}^{\sqrt{99}+\sqrt{97}} \) ✏️ Solution \( = \left(\frac{a}{b}\right)^{(\sqrt{99}-\sqrt{97})(\sqrt{99}+\sqrt{97})} \) \( = \left(\frac{a}{b}\right)^{99 – 97} \) \( = \left(\frac{a}{b}\right)^2 \) Final Answer: \( \boxed{\left(\frac{a}{b}\right)^2} \) Next Question / Full Exercise

If (6x)^6 = 6^8, Find x 🎥 Watch Video Solution Q. If \( (6x)^6 = 6^8 \), find \( x \) ✏️ Solution \( (6x)^6 = 6^6 \cdot x^6 \) \( 6^6 \cdot x^6 = 6^8 \) \( x^6 = 6^{8-6} \) \( x^6 = 6^2 \) \( x = 6^{\frac{2}{6}} \) \( x =

4 × (256)^(-1/4) ÷ (243)^(1/5) Solution 🎥 Watch Video Solution Q. Find the value of \( 4 \times (256)^{-\frac{1}{4}} \div (243)^{\frac{1}{5}} \) ✏️ Solution \( = 4 \times (2^8)^{-\frac{1}{4}} \div (3^5)^{\frac{1}{5}} \) \( = 4 \times 2^{-2} \div 3 \) \( = 4 \times \frac{1}{4} \div 3 \) \( = 1 \div 3 \) \(

If 6^n = 1296, Find 6^(n−3) 🎥 Watch Video Solution Q. If \( 6^n = 1296 \), find \( 6^{n-3} \) ✏️ Solution \( 1296 = 6^4 \) \( \therefore 6^n = 6^4 \) \( \Rightarrow n = 4 \) \( 6^{n-3} = 6^{4-3} \) \( = 6^1 \) \( = 6 \) Final Answer:

x = 8^(2/3) × 32^(-2/5), Find x^(-5) 🎥 Watch Video Solution Q. If \( x = 8^{\frac{2}{3}} \times 32^{-\frac{2}{5}} \), find \( x^{-5} \) ✏️ Solution \( x = (2^3)^{\frac{2}{3}} \times (2^5)^{-\frac{2}{5}} \) \( = 2^{2} \times 2^{-2} \) \( = 2^{2-2} \) \( = 2^0 \) \( = 1 \) \( \therefore x^{-5} =