Exponents and Squared Numbers

Exponents and Squared Numbers

Definition of Exponents

• Exponents are a shorthand way to represent repeated multiplication of a number by itself
• Expressed as a^n, where a is the base and n is the exponent or power
• The exponent indicates how many times the base is multiplied by itself

Squared Numbers

• A squared number is a number raised to the power of 2
• Expressed as a^2, where a is the base
• Example: 2 squared, or 2^2, is equivalent to 2 × 2 = 4

Properties of Exponents

• Product of Powers: a^m × a^n = a^(m+n)
• Power of a Product: (ab)^n = a^n × b^n
• Power of a Power: (a^m)^n = a^(mn)

Examples of Squared Numbers

• 3^2 = 3 × 3 = 9
• 4^2 = 4 × 4 = 16
• 5^2 = 5 × 5 = 25

Exponents and Squared Numbers

Definition of Exponents

• Exponents represent repeated multiplication of a number by itself in a concise way
• The notation a^n represents the base a multiplied by itself n times

Squared Numbers

• A squared number is a number raised to the power of 2, denoted as a^2
• It is equivalent to multiplying the base a by itself
• For example, 2 squared, or 2^2, is equal to 2 × 2 = 4

Properties of Exponents

Product of Powers

• When multiplying two exponential expressions with the same base, add the exponents: a^m × a^n = a^(m+n)

Power of a Product

• When raising a product to a power, raise each factor to that power: (ab)^n = a^n × b^n

Power of a Power

• When raising a power to another power, multiply the exponents: (a^m)^n = a^(mn)

Examples of Squared Numbers

• 3^2 is equal to 3 × 3, which equals 9
• 4^2 is equal to 4 × 4, which equals 16
• 5^2 is equal to 5 × 5, which equals 25