In this Grade 8 lesson from Reveal Math, Course 3, students learn how to use integer exponents to express repeated multiplication of rational numbers as powers, identifying the base and exponent in expressions involving integers, fractions, and negative numbers. The lesson covers writing both numerical and algebraic products in exponential form, including how parentheses affect the value of expressions with negative bases such as the difference between (-3)⁴ and -3⁴. Students also practice evaluating powers using the order of operations.
Section 1
Introduction to Exponents
An exponent is a number that appears above and to the right of a particular factor. It tells us how many times that factor occurs in the expression. The factor to which the exponent applies is called the base, and the product is called a power of the base.
An exponent indicates repeated multiplication.
where is a positive integer.
Section 2
Evaluating Exponents with Negative Bases
The placement of parentheses completely changes the meaning and the result of an expression with a negative base.
In , the base is and the entire negative number is multiplied times.
In , the base is just ; the exponent is applied first, and then the negative sign is attached to the final result.
Substitute with parentheses: .
Parentheses act like a protective force field! When you write , you're telling the math world to square the entire thing inside, negative sign and all, resulting in a positive 25. But without that force field, means you only square the 5, and the negative sign just waits outside to get tacked on at the very end. Always use parentheses when substituting negative numbers!
Section 3
Powers of Fractions
To raise a fraction to a power, write it as repeated multiplication or raise both the numerator and the denominator to that power:
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Section 1
Introduction to Exponents
An exponent is a number that appears above and to the right of a particular factor. It tells us how many times that factor occurs in the expression. The factor to which the exponent applies is called the base, and the product is called a power of the base.
An exponent indicates repeated multiplication.
where is a positive integer.
Section 2
Evaluating Exponents with Negative Bases
The placement of parentheses completely changes the meaning and the result of an expression with a negative base.
In , the base is and the entire negative number is multiplied times.
In , the base is just ; the exponent is applied first, and then the negative sign is attached to the final result.
Substitute with parentheses: .
Parentheses act like a protective force field! When you write , you're telling the math world to square the entire thing inside, negative sign and all, resulting in a positive 25. But without that force field, means you only square the 5, and the negative sign just waits outside to get tacked on at the very end. Always use parentheses when substituting negative numbers!
Section 3
Powers of Fractions
To raise a fraction to a power, write it as repeated multiplication or raise both the numerator and the denominator to that power:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter