Exponents

Exponent

A mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Square Root

A value that, when multiplied by itself, gives the original number; indicated by the radical symbol (√).

Product Rule

When multiplying exponents with the same base, add the powers: a^m * a^n = a^(m+n).

Quotient Rule

When dividing exponents with the same base, subtract the powers: a^m / a^n = a^(m-n).

Power Rule

When raising an exponent to another power, multiply the powers: (a^m)^n = a^(m*n).

Zero Exponent Rule

Any non-zero base raised to the power of zero is equal to one: a^0 = 1 (where a ≠ 0).

Negative Exponent Rule

A base raised to a negative exponent is equal to its reciprocal with a positive exponent: a^-n = 1/a^n.

Fractional Exponents

Represent a combination of powers and roots: a^(m/n) = (√[n]{a})^m = √[n]{a^m}.

Radical

An expression that includes a root, such as a square root or cube root, denoted by the radical sign (√).

Radicand

The number or expression underneath a radical sign.

Principal Square Root

The non-negative root of a number, represented by the square root symbol √.

Perfect Square Factor

A whole number that can be expressed as the product of an integer with itself.

Distributing Exponents

The incorrect process of applying an exponent to individual terms in an addition or subtraction: (a+b)^n ≠ a^n + b^n.

Simplifying Radicals

Breaking down a radical into its simplest form by identifying and removing perfect square factors.

Reciprocal

The multiplicative inverse of a number; if a ≠ 0, then the reciprocal of a is 1/a.

Exponential Form

A way of expressing numbers using a base and an exponent, such as a^b.

Radical Form

A way of expressing numbers using a radical sign, such as √a.

Binomial Theorem

A formula that provides a way to expand expressions that are raised to a power, represented as (a+b)^n.

Like Bases

Bases in an expression that are the same, allowing for the application of exponent rules.

Variable Exponents

Exponents that consist of a variable instead of a specific number.

Exponentiation

The mathematical operation involving an exponent; raising a base to a power.