Math 8 Chapter 1 Review

Powers and Exponents

100

Write the expression using exponents.

2*2*2*2*7*7*7*7*7*7

2^4*7^6

200

Evaluate the expression 

9^2+2^4

9*9+2*2*2*2

81+16

=97

300

Write the expression using exponents

(-10)*(-10)*3*3*3*3*3

(-10)^2*3^5

400

Evaluate the expression

15-(-2)^3

15-(-2)*(-2)*(-2)

15-(-8)

15+8

=23

500

Evaluate when x=-2 and y=1

x^4-y^3 

(-2)^4-(1)^3

-2*-2*-2*-2-1*1*1

16-1

=15

Multiply and Divide Monomials

100

Simplify the expression

5^3*5^6

5^(3+6)

=5^9

200

Simplify the expression

(h^12)/(h^4)

h^(12-4)

h^8

300

Simplify the expression 

4m^2*7m^11

Multiply the constants then add the exponents 

4*7=28

2+11=13

=28m^13

400

Simplify the expression 

(45p^10)/(15p^6)

Divide constants then subtract exponents 

45/15=3

10-6=4

3p^4

500

Simplify the expression 

(2^9*6^4*3^11)/(2^2*6^3*3^11

Break up into common bases then subtract exponents

(2^9/2^2)*(6^4/6^3)*(3^11/3^11)

9-2=7, 4-3=1, 11-11=0

2^7*6^1*3^0

Powers of Monomials

100

Simplify the expression 

(3^8)^4

3^(8*4)

=3^32

200

Simplify the expression

(m^3)^13

m^(3*13)

=m^39

300

Evaluate the expression

(5k^7)^2

Distribute the 2 to each term (5) and k^7

5^2*(k^7)^2

5*5*k^(7*2)

=25*k^14

400

Evaluate the expression 

(-2x^9y^6)^3

Distribute the 3 to each term (-2), (x^9), (y^6)

(-2)^3*(x^9)^3*(y^6)^3

-2*-2*-2*(x^(9*3))*(y^(6*3))

=(-8)*x^27*y^18

500

Evaluate the expression

(2x^11y^4z^10)^8

Distribute the 8 to each term

2^8*(x^11)^8*(y^4)^8*(z^10)^8

2*2*2*2*2*2*2*2*(x^(11*8))*(y^(4*8))*(z^(10*8))

=256*x^88*y^32*z^80

Zero and Negative Exponents

100

Simplify the expression

157^0

Anything besides 0, with a zero exponent equals 1!

=1

200

Simplify the expression, w doesn't equal 0

w^0

=1

300

Express using a positive exponent 

6^-4

=1/(6^4)

400

Express using a negative exponent 

1/(d^12)

=d^-12

500

Simplify the expression in SIMPLEST form

b^3*b^-7

Product of Powers: add exponents

b^(3+ -7)

=b^-4

=1/b^4

Scientific Notation and Standard Form

100

Write the number in standard form 

6.2X10^4

Positive exponent = move decimal to the right 

=62,000

200

Write the number in standard form

3.95X10^6

Positive exponent = move decimal to right 

=3,950,000

300

Write the number in scientific notation

2,876,000

Number is larger than 10 = positive exponent 

2.876X10^6

400

Write the number in scientific notation

0.00000000071

Number is between 0 and 1 = negative exponent 

=7.1X10^-10

500

A calculator screen shows.... write the number in standard form

4.927E-8

E represents X10, number after E is the exponent 

4.927X10^-8

=.00000004927