Grade 8 M1 Topic A Review

Lesson 1

100

Simplify.

{4 x ... x 4} 

   7 times

 

4⁷

200

Simplify.

{(-11.63) x ... x (-11.63)} 

            34 times

(-11.63)³⁴

300

Simplify.

{(-1/14) x ... x (-1/14)} 

          10 times

(-1/14)¹⁰

400

Simplify.

{x⋅x...x} 

185 times

x¹⁸⁵

500

Simplify.

{x⋅x...x} = xⁿ

    ^{______ times}

n times

Lesson 1-2

100

2x² • 3x⁹

6x¹¹

200

8a⁵ • 2y³

16a⁵y³

300

3x³z • 4x³y

12x⁶zy

400

12xy² 

-------

3x⁴y²

4

--

x³

500

4x⁵y³

------

20x³y⁴

x²

-----

5y

Lesson 1-3

100

(9³)⁶ =

9¹⁸

200

4⁸

--

5⁸

(4/5)⁸

300

(113² x 37 x 51⁴)³ =

113⁶ x 37³ x 51¹²

400

Let x,y,z be numbers. 

(x²yz⁴)³ =

x⁶y³z¹²

500

Let x,y,z be numbers and let m,n,p,q be positive integers. 

(x^myⁿz^p)^q

x^mqy^nqz^pq

Lesson 1-4

100

y¹² / y¹² =

y^12-12 = y⁰ = 1

200

9¹⁵ x (1 / 9¹⁵) = 

9¹⁵ / 9¹⁵ = 9^15-15 = 9⁰ = 1

300

Simplify the following expression as much as possible.

(4¹⁰ / 4¹⁰) x 7^{0 =} 

1

400

x⁴¹                y¹⁵

--       x     --        = 

y¹⁵                x⁴¹

x⁴¹y¹⁵              x⁴¹                  y¹⁵

-------     =   --        x     --        = x⁰y⁰ = 1x1 = 1

y¹⁵x⁴¹              x⁴¹                  y¹⁵

500

Let a and b be two numbers. Use the distributive law and then the definition of zeroth power to show that the numbers (a⁰ + b⁰)a⁰ and (a⁰ + b⁰)b⁰ are equal.

(a⁰ + b⁰)a⁰= a⁰ x a⁰ + b⁰ x a⁰ = a⁰⁺⁰ + a⁰b⁰

= 1 + 1 x 1 = 1 + 1 = 2

 (a⁰ + b⁰)b⁰ = a⁰ x b⁰ + b⁰ x b⁰ = a⁰b⁰ + b⁰⁺⁰

= 1 x 1 + 1 = 1 + 1 = 2

Since both numbers are equal to 2, they are equal.

Lesson 1-5

100

Let f be a nonzero number.

f^-4 = ?

1 / f⁴

200

671 x 28796^-1 = 

671/28796 or .0233

300

Compute 3³ x 3² x 3¹ x 3⁰ x 3^-1 x 3^-2

3³ = 27

400

Show that (17.6^-1)⁸ = 17.6^-8

By the power to a power rule:

(17.6^-1)⁸ = 17.6^{-1 x 8} = 17.6^-8

By the negative power rule:

(17.6^-1)⁸ = (1/17.6)⁸ = 1⁸ / 17.6⁸ 

= 1 / 17.6⁸ = 17.6^-8

500

Show that (2.8^-5 / 2.8⁷) = 2.8^-12

2.8^-5 = 1/2.8⁵

1/2.8⁵ x 1/2.8⁷ = 1/(2.8⁵ x 2.8⁷) = 1/2.8¹² = 2.8^-12