By Charlotte Johnson Updated Aug 30, 2022

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Mastering roots and exponents is foundational in algebra and is essential for advanced studies and many STEM careers. Below are clear, step‑by‑step rules to simplify expressions involving powers and radicals.

Step 1

Any expression raised to the first power stays the same: a¹ = a.

Step 2

When multiplying terms with the same base, add their exponents: y³·y⁴ = y⁷.

Step 3

Multiplying a power by a constant does not affect the exponent: 3·x² = 3x².

Step 4

In division, subtract exponents of like bases: a⁵ / a² = a³.

Step 5

Any expression raised to the zero power equals one: a⁰ = 1.

Step 6

Negative exponents represent reciprocals: x⁻³ = 1/x³.

Step 7

When a root sign is present, divide the exponent by the root index: √(x³) = x^(3/2).

Step 8

The square root of a product equals the product of the square roots: √(xy) = √x·√y.

Step 9

The square root of a quotient equals the quotient of the square roots: √(x/y) = √x/√y.

Follow these rules to confidently simplify algebraic expressions involving roots and exponents.