Chapter 10

Numbers

100

4^((5*-2)/2)

1/4^5

1/1024

200

-(16)^(5/4)

-32

300

(2^-1/2^-2)^-2

1/4

400

(2^-2/2^(-3/6))^(-4/3)/2

2

500

((2^(2^2)/2^2)-(2^(2)/(2^2+2^2+2^2+2))^-1)^-1

2

Letters

100

(\root[n](b+n))^n-(b+n)

0

200

((a+b)^-b/(a+b)^(-a))(a+b)

(a+b)^(a-b+1)

300

((b+c)rootx(x))/(brootx(x)+crootx(x))^x

(b+c)^(1-x)x^((1-x)/x)

400

((w^-wb^zx)/(wb^-zx^z))^(-wbx)/(w^((wbx+bx)w)b^(-bxwz)x^(-wbx)

b^3x^(wbxz)

500

((a^(b^c))^-b/root(b^c)(a^(b^c)))^-a

a^(a+ab^(1+c))

Letters & Numbers

100

(x^3/y^4)^(-1/3)

y^(4/3)/x

200

(-3sqrt(6xy^3))sqrt(6y)

-18y^2sqrtx

300

root3(108x^4y^8)

3xy^2root3(4xy^2)

400

(4sqrt(8x)-sqrt(2y^4))(sqrt(8x)+3sqrt(2y^4))

32x+44y^2sqrtx-6y^4

500

(4(R^4/R^(2+1))root3(24)+3Rroot3(3))R-2root3(81R^6)

5R^2root3(3)

Scientific notation

100

Write in Scientific notation

540000000

5.4*10^8

200

Write in scientific notation

0.000000032

3.2*10^-8

300

Perform the calculation in scientific notation

(40,000,000*300,000)/0.3

4*10^13

400

Preform the calculation

4.5*(4,000,000)^(3/2)/(9,000,000)

2000

2*10^3

500

Perform the calculation

((0.00004*300)/(0.00002))^(-3)

6*10^-6

Random

100

Simplify:

2sqrt50-4sqrt18-9sqrt32

-38sqrt2

200

Simplify:

(2sqrta+sqrtb)(3sqrta-4sqrtb)

6a-5sqrt(ab)-4b

300

Solve

sqrt(t^2+9t-1)=3

x=-10 &1

400

Solve (and check the answer!!!): 

sqrt(x+1)-sqrt(2x)=-1

Only

x=8

500

The formula

S=sqrt(30Df)

 is used to approximate the speed S, where D represents the length of the skid marks in feet and f represents the coefficient of friction for the road surface. Suppose that the coefficient of friction is 0.38. How far will a car skid, to the nearest foot, when the brakes are applied at 75 miles per hour?

75^2/(3*3.8)

or 493 feet