what is the value of x in the rational equations ⅓=⁴/x⅙?
Answer (1)
Answer:1. Simplify the Right Side: - ⁴/x⅙ = ⁴ * x⁻⅙ (Remember that a number raised to a negative exponent is the same as its reciprocal) 2. Rewrite the Equation: - ⅓ = ⁴ * x⁻⅙ 3. Isolate x⁻⅙: - Divide both sides by 4: (⅓) / 4 = x⁻⅙- Simplify: ¹/₁₂ = x⁻⅙ 4. Use Exponent Properties: - To get rid of the negative exponent, take the reciprocal of both sides: ₁₂ = x⅙ 5. Solve for x: - Raise both sides to the power of 6: ₁₂⁶ = (x⅙)⁶- Simplify: ₁₂⁶ = x- Calculate: x = 2985984 Therefore, the value of x is 2985984.
