University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

150

Pages:

2
Author:

Brent Cantu

Workshop #16 1. (a) What is the deﬁnition of √ 3 2? (b) Suppose a is a real number, how do we deﬁne √ 3 a? √ 1 (c) Use the rules of exponenets to show that it makes sense to write x 3 as 3 x. Your explanation must be good enough to convince your facilitator. √ √ √ 2. Is a + b = a + b always true? Choose numbers a and b to support your answer. 1 3. Write x− 2 in at least four diﬀerent, but equivalent ways. 1 1 4. Compute (43 ) 2 and (4 2 )3 by hand. Which is easier? 5. Compute the following without a calculator. Use the Super Helpful Property to make your life easier. 3 1 2 1 6 (d) 3 3 · 3 3 (a) 16 2 2 (e) 4 4 · 2 4 (b) 8 3 − 3 2 25 (c) 4 6. Simplify the following (a) (125z 3 )2/3 (b) [(x + 1)2 ]1/2 7. Simplify the following with only positive exponents. Assume all variables are positive (a) x4 · x2 (c) (a3 )2 (b) x3/2 · x5/7 (d) (a2/3 )3/4 8. Simplify the following with only positive exponents. Assume all variables are positive z4 z2 z 3/2 (b) 5/7 z (c) (w3 y −3 )2 (a) (d) (w3/5 y 1/7 )3 9. Multiply the following and simplify the exponents (a) (x3 + 3x2 − 1) · x−1/2 10. Simplify the following √ √ (a) 7 7 √ √ √ 3 3 3 (b) 13 13 13 (b) y 3/5 · (y 2/5 + y 1/5 − y −3/5 ) √ √ 3 3 3 9 √ (d) 2700 (c) (c) (x1/2 + y 3/2 )2 11. Simplify the following assume all variables are positive values √ 3 32a5 3 7a (a) √ (c) 64 2a 26b−3 5x (d) 3 (b) y6 16z 4 12. Suppose that 2y 7 = 1.1. Without using a calculator, evaluate 8y 7 + 32y 7 − 2y 7 13. Simplify the following (a) √ 288 − √ 98 (b) 3 xy 4 + 3 8xy 4 − 3 27xy 4