115W Ch1 Review

Exponent and Scientific Notation

100

Simplify: (ab²)³

a³b⁶

200

Convert to scientific notation: 0.00526

5.26*10^-3

300

Multiply and write answer in scientific notation: (1.5*10^5)(6.8*10^-7)

1.02*10^13

400

Divide and write answer in scientific notation: (3*10⁶)/(6*10⁴)

5*10¹¹

500

Simplify: [(2h²*h³*k)⁴/(7h^-1*k²)²]²

256h⁴⁴/2401

Radicals and Rational Exponents

100

Simplify: -(289)^1/2

-17

200

Simplify: (18)^1/2*(15)^1/2

3(30)^1/2

300

Simplify (use absolute value sign if needed): [(45x⁵)/(y⁴)]^1/2

[3x²*(5x)^1/2]/(y²)

400

Simplify: (54)^1/3+3*(2)^1/3

6*(2)^1/3

500

Rationalize denominator (simplify): [(q)^1/2-(10)^1/2]/[(q)^1/2+(10)^1/2] (hint: leave final answer in factored form)

[(q)^1/2-(10)^1/2]²/(q-10)

Polynomials

100

Identify the degree, leading term, and leading coefficient: 7x-2x²+12

Degree: 2

Leading term: -2x^2

Leading coefficient: 

200

Simplify: (9w²-yw+5)-(-2w²-4)

11w²-yw+9

300

Simplify: (d²+2d)(3c+2)

3cd²+6cd+2d²+4d

400

Simplify: (2x²+3)²

4x⁴+12x²+9

500

Simplify:2-4i/1-3i

-1-i

Factor Polynomials

100

Use distributive property for factor: 14m³+70m²-105m

7m(2m²+10m-15)

200

Factor by grouping: 3s²+3s+2s+2

(3s+2)(s+1)

300

Factor using any method: t²+14t+24

(t+12)(t+2)

400

Factor: x³+512

(x+8)(x²-8x+64)

500

Factor: 8x³-125

(2x-5)(4x²+10x+25)

Rational Expressions

100

Simplify: (y²-4)/(y²+y-6)

(y+2)(y+3)

200

Simplify: (4x²-4x+1)/(2x+1)

2x-1

300

(5x²-3x-2)/(5x²-18x-8)

(x-1)/(x-4)

400

Factor: (m^2-6m)/(m^2-1)-(3m+2)/(1-m^2)

(m-2)/(m+1)

500

[(3/x)-(5/y)]/x

(3y-5x)/x²y