Algebraic Expressions: Exponents Part 1

Exponential Expressions and Evaluations

• "Five to the third power" is expressed as 5^3, which evaluates to 125 (5 x 5 x 5).
• "Six to the third power" is expressed as 6^3.
• "Seven to the fourth power" is expressed as 7^4.

Writing Exponents

• The variable x squared is written as x^2.
• The product of 3a taken three times is represented as (3a)^3.
• "r" repeated five times is expressed as r^5.

Combining Base and Exponents

• "Five repeated three times and b repeated four times" is written as 5^3b^4.
• For the expression combining 10, a, and b, it is expressed as 10^2a^2b.

Expanded Forms

• "Four repeated three times and a, b repeated twice" is written as 4^3a^2b^2.
• The number 5 squared can be represented in expanded form as 5 x 5.
• The expanded form of (-2) cubed is shown as (-2)(-2)(-2).
• The number 10 raised to the fourth power can be expressed as (10)(10)(10)(10).
• The expression for (-a) cubed is represented as (-a)(-a)(-a).

Importance of Parentheses

• Parentheses are crucial to indicate multiplication when expressing expanded forms.
• Clarifying negative bases requires parentheses for accurate representation in exponents.