Raising a Number to a Power
Raise numbers to powers in Grade 9 algebra. Evaluate expressions like 2³ and x⁴ through repeated multiplication and apply exponent rules to simplify algebraic power expressions.
Key Concepts
Property An even exponent on a negative base gives a positive result, while an odd exponent gives a negative result. Note the difference: $( a)^n$ is not the same as $ a^n$.
Examples $( 5)^2 = ( 5)( 5) = 25$ $( 5)^3 = ( 5)( 5)( 5) = 125$ $ 5^2 = (5 \cdot 5) = 25$.
Explanation Parentheses are VIP passes! In $( 3)^4$, the negative is included in the repeated multiplication, resulting in a positive. But in $ 3^4$, the negative is an outsider, applied only after the power is calculated, making the final answer negative. Always check if the negative sign is inside the parentheses to see if it gets to join the party!
Common Questions
What does it mean to raise a number to a power?
Raising a number to a power means multiplying it by itself a specified number of times. 2³ = 2 × 2 × 2 = 8. The base is 2, the exponent is 3, and 8 is the result.
What is the difference between the base and the exponent?
The base is the number being multiplied repeatedly. The exponent tells how many times to use the base as a factor. In 5⁴: 5 is the base, 4 is the exponent, 5 × 5 × 5 × 5 = 625.
How do you evaluate a negative base raised to a power?
A negative base with an even exponent gives a positive result: (-2)⁴ = 16. An odd exponent gives negative: (-2)³ = -8. Without parentheses, -2⁴ means -(2⁴) = -16.