1. ALGEBRA READINESS LESSON 10-2 Warm Up Lesson 10-2 Warm-Up

2. ALGEBRA READINESS LESSON 10-2 Warm Up Lesson 10-2 Warm-Up

3. ALGEBRA READINESS “Power Rules” (10-2) What happens when you raise a power to a power? Rule: When you raise a power to a power [Example: (a m ) n ], multiply the powers together. Example: (7 2 ) 3 = (7 2 ) · (7 2 ) · (7 2 ) = (7 · 7) · (7 · 7) · (7 · 7) = 7 6 Example: (a 6 ) 2 = a 6 · a 6 = (a · a · a · a · a · a) · (a · a · a · a · a · a) = a 12 (a m ) n · a mn

4. ALGEBRA READINESS Write the expression using a single exponent. a. (5 –2 ) 3 b. (8 –4 ) –5 Multiply the exponents. = 5 (–2 3) = 8 (–4 –5) Simplify the exponent. = 5 –6 = 8 20 = 156156 Write with a positive exponent. Power Rules LESSON 10-2 Additional Examples

5. ALGEBRA READINESS Simplify b 2 (b 3 ) –2. b 2 (b 3 ) –2 = b 2 b 3 (–2) Multiply exponents in (b 3 ) –2. = b 2 + (–6) Add exponents when multiplying powers of the same base. Simplify. = b –4 = b 2 b –6 Simplify. 1 b 4 = Write using only positive exponents. Power Rules LESSON 10-1 Additional Examples

6. ALGEBRA READINESS What happens when you raise a product (for example, a variable and a coefficient, like 4x) to a power? Rule: When you raise a product to a power (Example: ab m, where a and b are nonzero numbers), raise each multiplicand (a and b) to the power separately. Example: (3x) 4 = 3 4 x 4 = 3 · 3 · 3 · 3 · x 4 = 81x 4 Example: ab n = a n · b n “Power Rules” (10-2)

7. ALGEBRA READINESS Simplify (4x 3 ) 2. (4x 3 ) 2 = 4 2 (x 3 ) 2 Raise each factor to the second power. = 4 2 x 6 Multiply exponents of a power raised to a power. = 16x 6 Simplify. Power Rules LESSON 10-2 Additional Examples

8. ALGEBRA READINESS Use the formula for the area of a circle, A = r 2, to find the area of a circle with a radius of 4  10 –2 m. Use 3.14 for. A = r 2 = 3.14 (4  10 –2 ) 2 Substitute into the formula. = 3.14 4 2  (10 –2 ) 2 Raise the product to a power. = 3.14 16  10 –4 Raise the power to a power. = 50.24  10 –4 Multiply. = 0.005024 Simplify. The area of the circle is about 0.005024 m 2. Power Rules LESSON 10-2 Additional Examples

9. ALGEBRA READINESS 1. Write (9 –3 ) 8 using a single exponent. 2. Simplify (2a 6 ) 3. 3. Find the area of a circle whose radius is 5  10 –7 m. Use 3.14 for. 9 –24 or 1 9 24 8a 18 7.85  10 –13 m 2 or 0.000000000000785 m 2 Power Rules LESSON 10-2 Lesson Quiz