May 2026

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} =

(169^-3 / 196^-8)^(1/48) Solution 🎥 Watch Video Solution Q. Find the value of \( \left(\frac{169^{-3}}{196^{-8}}\right)^{\frac{1}{48}} \) ✏️ Solution \( = \left(\frac{(13^2)^{-3}}{(14^2)^{-8}}\right)^{\frac{1}{48}} \) \( = \left(\frac{13^{-6}}{14^{-16}}\right)^{\frac{1}{48}} \) \( = \left(13^{-6} \times 14^{16}\right)^{\frac{1}{48}} \) \( = 13^{-\frac{6}{48}} \times 14^{\frac{16}{48}} \) \( = 13^{-\frac{1}{8}} \times 14^{\frac{1}{3}} \) \( = \frac{14^{1/3}}{13^{1/8}} \) Final Answer: \( \boxed{\dfrac{14^{1/3}}{13^{1/8}}} \) Next Question

81^(1/4) × 9^(3/2) × 27^(-4/3) Solution 🎥 Watch Video Solution Q. Find the value of \( 81^{\frac{1}{4}} \times 9^{\frac{3}{2}} \times 27^{-\frac{4}{3}} \) ✏️ Solution \( = (3^4)^{\frac{1}{4}} \times (3^2)^{\frac{3}{2}} \times (3^3)^{-\frac{4}{3}} \) \( = 3^{1} \times 3^{3} \times 3^{-4} \) \( = 3^{1+3-4} \) \( = 3^0 \) \( = 1 \) Final Answer: \(

(21² − 15²)^(2/3) Solution 🎥 Watch Video Solution Q. Find the value of \( (21^2 – 15^2)^{\frac{2}{3}} \) ✏️ Solution \( (21^2 – 15^2)^{\frac{2}{3}} \) \( = (441 – 225)^{\frac{2}{3}} \) \( = (216)^{\frac{2}{3}} \) \( = (6^3)^{\frac{2}{3}} \) \( = 6^{2} \) \( = 36 \) Final Answer: \( \boxed{36} \) Next Question /