Powers and Exponents
Perfect Squares
Perfect Cubes
Challenging Powers & Exponents Problems
Challenging Perfect Squares & Perfect Cubes Problems
100

What's the base (big number) and what's the exponent (small number)? 23

the exponent is 3 and the base is 2. 

100

Is 366 a perfect square?

No

100

What does the word cubed mean? 

raised to the third power

100

Evaluate 172

289

100

Is 196 a perfect square, perfect cube, or neither?

perfect square

200

What is 7in expanded form? 

7x7x7

200

What is 62?

36

200

What is 23?

8

200

Evaluate 73

343

200

Is 1 a perfect square, a perfect cube, or neither?

It is BOTH a perfect square and a perfect cube.

300

Write 32 in word form. 

three to the second power OR three squared

300

Is 324 a perfect square? If yes, write the number as a whole number squared? 


(Ex: 36; 62)

Yes; 182

300

Is 64 a perfect square, perfect cube, both, or neither? 

perfect square AND a perfect cube

300

Evaluate four cubed. 

64

300

Is 169 a perfect square? If so, write the number as a whole number squared. 


(ex: 49=> 72)

yes; 132

400

4x4x4x4x4 is what in exponential form? 

45

400

Which of the following numbers are perfect squares and divisible by 4?

12, 16, 24, 100, 167

(there are only 2 numbers for your answers)

16,100

400

Which of the following are perfect cubes? 

(there are only 2 answers)

1, 9, 27, 49, 66

1 and 27

400

Is 56 < (less than), > (greater than), or = (equal to) to 105

< (less than)

400

Which of the following numbers is a perfect square and is divisible by 3? 

(3, 9, 40, 144, 242)

9 and 144

500

Is 15< (less than), > (greater than), or = (equal) to 72

> (greater than)

500

14 is between ______2 and ________2

3 and 4

500

108 is between ____2 and _____2.

10 and 11

500

Evaluate 82 x 25

2,048

500

340 is between _____2 and _______2

18 and 19

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