Page 91 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

B2.2 Powers
analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressions
Teacher supports
Examples
• simplifying operations with powers by examining patterns in the expanded forms of powers: o product of powers (addition of exponents):
• 35×32=(3×3×3×3×3)×(3×3)=3(5+2)=37 • 35×3−2=(3×3×3×3×3)× 1 =35+(−2)=33
3×3
• ax×ay=ax+y
o quotient of powers (subtraction of exponents): • 45 =4×4×4×4×4
43 4×4×4
=4×4
= 42
o power of a power (multiplication of exponents):
• (52)3=52×52×52=(5×5)×(5×5)×(5×5)=56 • (ax)y=a(x×y)
• numeric expressions:
o expressions composed of rational bases and integer exponents; for example, 2−4 × 25, 107 ÷ 105, ((1)2)4, (−2.3)5 × (−2.3)−2
3 (−2.3)3
• algebraic expressions:
o expressions involving integer exponents; for example, x5 × x−2, (y−2)2, (xy2)2, x−3 × x4
Instructional Tips
Teachers can:
• emphasize the reasoning behind the relationships between multiplication, division, and power of a power involving exponents;
• use numeric expressions based on real-life examples to highlight bases that are commonly used (e.g., base 10 in scientific notation);
• organize the learning in stages to develop students’ understanding of the relationships (e.g., begin the learning with exponents that are positive integers and then move to negative integers; begin with simplifying numeric expressions and then move to algebraic expressions);
• consider connecting the learning in this expectation to future learning about domain; for example,
90
x2