In this Grade 8 lesson from Yoshiwara Core Math Chapter 3, students learn exponential notation, including how to identify the base and exponent, write repeated multiplication as a power, and evaluate expressions such as 2 to the fifth or 3 to the fifth. The lesson covers squaring and cubing numbers in the context of area and volume, and connects exponent skills to the Pythagorean theorem. Students practice with whole numbers, fractions, and decimals to build fluency with powers and avoid common mistakes like confusing exponents with multiplication.
Section 1
📘 Exponents
Exponents are a powerful shorthand for repeated multiplication. In this lesson, we'll master this notation to calculate powers, find areas and volumes, and explore the famous Pythagorean theorem, which connects the sides of a right triangle.
Now, let’s dive into worked examples. You'll soon apply these concepts with interactive practice cards and solve challenge problems on the Pythagorean theorem.
Section 2
A New Notation
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 product. The factor to which the exponent applies is called the base, and the product is called a power of the base. For example, we can write 32 as .
Section 3
Squares and Cubes
The exponents 2 and 3 are used frequently, so they have special names.
Section 4
Powers Before Products
Rule: Compute powers before multiplications or divisions.
If we want to multiply before computing the power, we must use parentheses around the product. The parentheses tell us to simplify what’s inside first.
Section 5
Pythagorean Theorem
A triangle in which one of the angles is a right angle, or , is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs.
If stands for the length of the hypotenuse, and the lengths of the two legs are and , then:
In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
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Section 1
📘 Exponents
Exponents are a powerful shorthand for repeated multiplication. In this lesson, we'll master this notation to calculate powers, find areas and volumes, and explore the famous Pythagorean theorem, which connects the sides of a right triangle.
Now, let’s dive into worked examples. You'll soon apply these concepts with interactive practice cards and solve challenge problems on the Pythagorean theorem.
Section 2
A New Notation
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 product. The factor to which the exponent applies is called the base, and the product is called a power of the base. For example, we can write 32 as .
Section 3
Squares and Cubes
The exponents 2 and 3 are used frequently, so they have special names.
Section 4
Powers Before Products
Rule: Compute powers before multiplications or divisions.
If we want to multiply before computing the power, we must use parentheses around the product. The parentheses tell us to simplify what’s inside first.
Section 5
Pythagorean Theorem
A triangle in which one of the angles is a right angle, or , is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs.
If stands for the length of the hypotenuse, and the lengths of the two legs are and , then:
In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter