Evaluating Algebraic Expressions with Exponents
Evaluate algebraic expressions with exponents in Grade 9. Substitute values for variables, apply PEMDAS to compute powers first, then multiply and add to find the result.
Key Concepts
Property To evaluate expressions with exponents, substitute the given values, then simplify using the order of operations (PEMDAS), paying close attention to parentheses and powers.
Examples Evaluate $2(z y)^2 3y^2$ for $z = 5, y = 3$. $2(5 3)^2 3(3)^2 = 2(2)^2 3(9) = 8 27 = 19$. Evaluate $a^3 + (b a)^2$ for $a = 2, b = 7$. $(2)^3 + (7 2)^2 = 8 + (5)^2 = 8 + 25 = 33$.
Explanation When exponents join the party, they get VIP treatment! Always solve the powers right after substituting your numbers, especially those inside parentheses. This ensures everything else in the equation gets calculated in the correct, orderly fashion, preventing mathematical chaos and leading to the right answer.
Common Questions
How do you evaluate an algebraic expression with exponents?
Substitute the given value for each variable, then use PEMDAS: evaluate exponents first, then multiply/divide, then add/subtract. For 3x² when x = 4: 3(4²) = 3(16) = 48.
Why is 3x² different from (3x)²?
3x² means 3 times (x squared): the exponent applies only to x. (3x)² means (3x) squared = 9x². Parentheses determine what gets squared.
What is a common mistake when evaluating with negative values and exponents?
When substituting a negative value, use parentheses. For x = -2 in x²: write (-2)² = 4. Without parentheses, -2² = -(2²) = -4, which incorrectly negates the result.