Module 3 Test Review

Exponent Rules

100

Simplify (3a^2b^-3)^-4 

b^12/(81a^8)

200

Simplify x^(3/2)/x^(5/2) 

1/x

300

Simplify ((2a^(-1)b^5)/(4a^4))^3 

b^15/(8a^9)

400

 Simplify (1/2x^(-10)y^8z^(1/3))^(-4) 

(16x^40)/(y^32z^(4/3)

500

Simplify (x^(1/4)y^(-2)z^3z^(1/4))/(x^(3/5)y^(1/2) 

z^(13/4)/(x^(7/20)y^(5/2)

Exp & Log Form

100

Rewrite in exponential form \log_x144=2 

x^2=144

200

Rewrite in exponential form \log_(1/2)16=y 

(1/2)^y=16

300

 Rewrite in exponential form 3\log_7x=18 

7^6=x

400

Rewrite in logarithmic form 12\cdot7^(5x+3)=24 

\log_7 2=5x+3

500

Rewrite in logarithmic form y\cdot x^(-2x+1)=y^2 

\log_x y=-2x+1

Scientific Notation

100

Multiply  (4.73\times10^(-2))(6.82\times 10^5) 

3.226\times 10^4

200

Divide  (8.13\times10^6)/(1.23\times10^(-4) 

6.61\times 10^10

300

Add  (7.34\times 10^(-2))+(2.11\times10^(-1)) 

2.844\times 10^(-1)

400

Simplify  ((4.78\times10^15)(3.22\times10^(-2)))/(7.58\times10^2) 

2.03\times10^11

500

Simplify  (5.51\times10^3)-(4.73\times10^2)+(2.23\times10^4)  

2.734\times10^4

Log Properties

100

Expand  \log_2(7\cdotx^2) 

\log_2 7+2\log_2x

200

Condense  3\log_5(15)-4\log_5(x) 

\log_5(15^3/x^4)

300

Condense  1/3\log x+2\log x+4\log x 

\logx^(19/3)

400

Expand  \log_8((x^4y^3)/z^(1/2))^5 

20\log_8x+15\log_8y-(5/2)\log_8z

500

Condense  1/2\log_3 4-2\log_3 5+\log_3 10 

\log_3(4/5)

Solving Logs

100

Solve for x.  \log(1/1000)=x 

x=-3

200

Solve for x.  \log_81 9=x 

x=1/2

300

Solve for x.  (1/3)^x=27 

x=-3

400

Solve for x (round to three decimal places).  4^(x+1)=70 

x=2.065

500

Solve for x (round to three decimal places).  -7\cdot8^(2x+3)=-55 

x=-1.005