Ravi Kant Kumar

(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 /

Find (x+1)^2 Question \[ (x-1)^3 = 8 \] Solution \[ 8 = 2^3 \] \[ (x-1)^3 = 2^3 \] \[ x – 1 = 2 \] \[ x = 3 \] \[ (x+1)^2 = (3+1)^2 \] \[ = 4^2 \] \[ = 16 \] Answer \[ \boxed{16} \] Next Question / Full Exercise

Simplify Step-wise Question \[ \left[\{625^{-1/2}\}^{-1/4}\right]^2 \] Solution \[ 625 = 5^4 \] \[ = \left[\{(5^4)^{-1/2}\}^{-1/4}\right]^2 \] \[ = \left[(5^{-2})^{-1/4}\right]^2 \] \[ = \left[5^{1/2}\right]^2 \] \[ = 5 \] Answer \[ \boxed{5} \] Next Question / Full Exercise

Find Value of Given Expression Question \[ \{5(8^{1/3}+27^{1/3})^3\}^{1/4} \] Solution \[ 8^{1/3} = 2,\quad 27^{1/3} = 3 \] \[ = \{5(2+3)^3\}^{1/4} \] \[ = \{5 \cdot 5^3\}^{1/4} \] \[ = \{5^4\}^{1/4} \] \[ = 5 \] Answer \[ \boxed{5} \] Next Question / Full Exercise

Find Value of ∛(125 × 27) Question \[ \sqrt[3]{125 \times 27} \] Solution \[ 125 = 5^3,\quad 27 = 3^3 \] \[ = \sqrt[3]{5^3 \times 3^3} \] \[ = \sqrt[3]{(15)^3} \] \[ = 15 \] Answer \[ \boxed{15} \] Next Question / Full Exercise

Convert to Rational Number Question \[ \left(\frac{1}{9}\right)^{-1/2} \times 64^{-1/3} \] Solution \[ \left(\frac{1}{9}\right)^{-1/2} = 9^{1/2} \] \[ = 3 \] \[ 64^{-1/3} = \frac{1}{64^{1/3}} \] \[ = \frac{1}{4} \] \[ = 3 \times \frac{1}{4} \] \[ = \frac{3}{4} \] Answer \[ \boxed{\frac{3}{4}} \] Next Question / Full Exercise

Find Value of ∛7 × ∛49 Question \[ \sqrt[3]{7} \times \sqrt[3]{49} \] Solution \[ = \sqrt[3]{7 \times 49} \] \[ 49 = 7^2 \] \[ = \sqrt[3]{7 \times 7^2} \] \[ = \sqrt[3]{7^3} \] \[ = 7 \] Answer \[ \boxed{7} \] Next Question / Full Exercise

Find x/y Question \[ 3^{x-1}=9,\quad 4^{y+2}=64 \] Solution \[ 9=3^2 \Rightarrow 3^{x-1}=3^2 \] \[ x-1=2 \Rightarrow x=3 \] \[ 64=4^3 \Rightarrow 4^{y+2}=4^3 \] \[ y+2=3 \Rightarrow y=1 \] \[ \frac{x}{y}=\frac{3}{1}=3 \] Answer \[ \boxed{3} \] Next Question / Full Exercise