Simplifying Exponential Expressions

Simplifying Expressions With Like Bases

• When simplifying exponential expressions with like bases, multiply the coefficients and add the exponents.
• Rule: a^m × a^n = a^(m+n)
• Example: 2^3 × 2^5 = 2^(3+5) = 2^8

Negative Exponents

• A negative exponent indicates the reciprocal of the base raised to the positive exponent.
• Rule: a^(-n) = 1/a^n
• Example: 2^(-3) = 1/2^3 = 1/8
• When simplifying expressions with negative exponents, rewrite the expression with positive exponents and then simplify.

Simplifying Expressions With Unlike Bases

• When simplifying exponential expressions with unlike bases, simplify each base separately.
• Rule: (a^m × b^n) = a^m × b^n (simplify each base separately)
• Example: 2^3 × 3^2 = (2 × 2 × 2) × (3 × 3) = 8 × 9 = 72
• When there are multiple unlike bases, simplify each base separately and then multiply the results.

Simplifying Expressions With Like Bases

• To simplify exponential expressions with like bases, multiply the coefficients and add the exponents.
• The rule to remember is: a^m × a^n = a^(m+n).
• For example, 2^3 × 2^5 is simplified to 2^(3+5) = 2^8.

Negative Exponents

• A negative exponent indicates the reciprocal of the base raised to the positive exponent.
• The rule to remember is: a^(-n) = 1/a^n.
• For example, 2^(-3) is equivalent to 1/2^3 = 1/8.
• When simplifying expressions with negative exponents, rewrite the expression with positive exponents and then simplify.

Simplifying Expressions With Unlike Bases

• When simplifying exponential expressions with unlike bases, simplify each base separately.
• The rule to remember is: (a^m × b^n) = a^m × b^n (simplify each base separately).
• For example, 2^3 × 3^2 is simplified to (2 × 2 × 2) × (3 × 3) = 8 × 9 = 72.
• When there are multiple unlike bases, simplify each base separately and then multiply the results.