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The nth Root and Fractional Indices

Numbers and Decimals The nth Root and Fractional Indices

🎬 Video Tutorial

The nth root of a number: The value that, when raised to the power of n, results in the original number. For example, the 4th root of 16 is 2, as 2⁴ = 16.
Fractional Indices Rule: Raising a number to the power of 1/n is the same as finding the nth root. For instance, 125^(1/3) = ∛125 = 5.
Combining Roots and Powers: For fractional exponents like 125^(2/3), first find the cube root of 125, then square the result to get 25.

📂 Revision Cards

Diagram explaining square, cube, and fourth roots. It shows the calculations for ²?9=3, ³?125=5, and ??16=2, with corresponding powers.

Rules of nth root illustrated with ³?8, showing that ³?8 is 2, and the relationship between nth roots and fractional indices with examples.

Equation showing the ³?125 equals 5, illustrating the relationship between fractional indices and nth roots. A side note shows 5 cubed equals 125.

Demonstration of the cube root of 125, showing that 125 raised to the power of 1/3 equals 5, alongside an illustration of 5 cubed equalling 125.

Fractional indices concept showing how to simplify 125^(2/3) = 25 using roots and powers, alongside the general formula a^(m/n) = (n?a)^m.

Equation showing fractional indices, with 16 raised to the power of 3/4 equalling the cube of the fourth root of 16, simplified to 2, resulting in 8.

Understanding the nth root and fractional indices with equations showing how fractional indices relate to nth roots.

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