Grade 8 - Unit 2: Exponents

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Addition Property of Equality

For real numbers a, b, and c, if a = b, then a + c = b + c. In other words, adding the same number to each side of an equation produces an equivalent equation.

Additive Inverse

The sum of a number and its additive inverse is zero. Also called the opposite of a number. Example: 5 and -5 are additive inverses of each other.

Algebraic Expression

A mathematical phrase involving at least one variable. Expressions can contain numbers and operation symbols.

Cube Root

If the cube root of a number b is a (i.e., 3b= a), then a3 = b.

Decimal Expression

The decimal expansion of a number is its representation in base 10 (i.e., the decimal system). For example, the decimal expansion of 252 is 625, of π is 3.14159..., and of 91 is 0.1111....

Equation

A mathematical sentence that contains an equals sign.

Evaluate an Algebraic Expressioin

To perform operations to obtain a single number or value.

Exponent

The number of times a base is used as a factor of repeated multiplication.

Inverse Operation

Pairs of operations that undo each other, for example, addition and subtraction are inverse operations and multiplication and division are inverse operations.

Irrational

A real number whose decimal form is non-terminating and non-repeating that cannot be written as the ratio of two integers.

Like Terms

Monomials that have the same variable raised to the same power. Only the coefficients of like terms can be different.

Linear Equation in One Variable

An equation that can be written in the form ax + b = c where a, b, and c are real numbers and a ≠ 0

Multiplication Property of Equality

For real numbers a, b, and c (c ≠ 0), if a = b, then ac = bc. In other words, multiplying both sides of an equation by the same number produces an equivalent expression.

Multiplicative Inverses

Two numbers that when multiplied together equal 1, for example, 4 and ¼.

Perfect Square

A number that has a rational number as its square root.

Radical

A symbol that is used to indicate square roots.

Rational

A number that can be written as the ratio of two integers with a nonzero denominator.

Scientific Notation

A representation of real numbers as the product of a number between 1 and 10 and a power of 10, used primarily for very large or very small numbers.

Significant Digits

A way of describing how precisely a number is written.

Solution

The value or values of a variable that make an equation a true statement

Solve

Identify the value that when substituted for the variable makes the equation a true statement.

Square Root

One of two equal factors of a nonnegative number. For example, 5 is a square root of 25 because 5 • 5 = 25. Another square root of 25 is -5 because (-5) • (-5) = 25. The +5 is called the principle square root of 25 and is always assumed when the radical symbol is used.

Variable

A letter or symbol used to represent a number.

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