Task Sets: Know and apply the properties of integer exponents - Common Core Math - Grade 8

A

Recall / Warm-Up

1.

Evaluate $2^5$ .

A.

10

B.

25

C.

32

D.

64

2.

Evaluate $3 \times 2^3$ .

A.

24

B.

11

C.

9

D.

6

3.

Which expression means the same as $4^3$ ?

A.

$4 \times 4 \times 4$

B.

$3 \times 4$

C.

$4 + 4 + 4$

D.

$3^4$

B

Fluency Practice

C

Varied Practice

$Flowchart showing simplification of 3 squared times 3 to the negative fifth into 3 to the negative third, then one over 27$

1.

Complete the simplification: $3^2 \times 3^{-5} = 3^{\_\_} = \_\_$ .

combined exponent:

final value:

2.

Which statement is correct about $2^3 \times 5^4$ ?

A.

It simplifies to $10^7$ by adding exponents

B.

It simplifies to $10^{12}$ by multiplying exponents

C.

You cannot combine exponents with one rule because the bases are different

D.

It simplifies to $2^7$

3.

Simplify $\dfrac{(6 \cdot 2)^3}{6^3}$ .

$Diagram showing that a negative exponent flips 5 over 2 to 2 over 5 and keeps exponent 3$

4.

Which expression is equivalent to $\left(\dfrac{5}{2}\right)^{-3}$ ?

A.

$\left(\dfrac{5}{2}\right)^3$

B.

$\left(\dfrac{2}{5}\right)^3$

C.

$-\left(\dfrac{5}{2}\right)^3$

D.

$\dfrac{5^3}{2}$

D

Word Problems

1.

A digital archive combines two folders that contain $10^6$ bytes and $10^4$ bytes of compressed units with the same base model.

Using exponent properties, which single power of 10 represents the product $10^6 \times 10^4$ ?

A.

$10^{2}$

B.

$10^{10}$

C.

$10^{24}$

D.

$20^{10}$

2.

A coding challenge uses the expression $\dfrac{(2^5)^2}{2^3}$ to represent the number of operations in a stage.

1.

Rewrite the expression as a single power of 2.

2.

Evaluate the expression as an integer.

3.

A simulation scales values by a factor of $9^0$ at one stage so the unit size stays unchanged.

What is the value of the scale factor $9^0$ ?

A.

0

B.

1

C.

9

D.

-1

E

Error Analysis

1.

Kai solved: $3^4 \times 3^2$

Kai's work:
$3^4 \times 3^2 = 3^{4\cdot2} = 3^8$

What is Kai's error?

A.

Kai used the quotient rule instead of the product rule

B.

Kai should have added exponents for a product with the same base

C.

Kai should have changed the base from 3 to 6

D.

Kai's work is correct

2.

Jordan solved: $5^{-2}$

Jordan's work:
$5^{-2} = -25$

Which correction is correct?

A.

$5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{25}$

B.

$5^{-2}=-(5^2)=-25$

C.

$5^{-2}=5^2=25$

D.

$5^{-2}=\dfrac{-1}{25}$

F

Challenge / Extension

$Step ladder simplifying a compound exponent expression to 4$

1.

Simplify completely and write with positive exponents only: $\dfrac{(2^3)^2 \cdot 2^{-5}}{2^{-1}}$

2.