Practice worksheet for calculating exponents, square roots, and cube roots, with instructions to show work and write "IMPOSSIBLE" if not possible.

Let’s go through each part step by step.

---

Part A: Exponents

We need to calculate powers. Remember:
- For positive bases, just multiply the base by itself as many times as the exponent says.
- For negative bases in parentheses like (-5)², you square the whole number including the sign.
- But if it’s written like -3² (without parentheses), that means “negative of 3 squared” — so first square 3, then apply the negative.

1) 2⁴ = 2 × 2 × 2 × 2 = 16
2) -3² = -(3 × 3) = -9 ← Important! No parentheses around -3, so only 3 is squared.
3) 4³ = 4 × 4 × 4 = 64
4) (-5)² = (-5) × (-5) = 25 ← Parentheses mean we square the negative too → positive result
5) 10³ = 10 × 10 × 10 = 1000
6) 12² = 12 × 12 = 144
7) (-8)³ = (-8) × (-8) × (-8) = 64 × (-8) = -512 ← Odd power keeps the negative sign
8) 7² = 7 × 7 = 49

✔ All checked.

---

Part B: Square Roots

Square root asks: “What number multiplied by itself gives this?”
But note: You cannot take the square root of a negative number using real numbers → write IMPOSSIBLE.

Also, √ means principal (positive) square root unless otherwise specified.

11) √16 = 4 → because 4×4=16 ✔
12) √25 = 5 → 5×5=25 ✔
13) √(-100) → Negative under root → IMPOSSIBLE ✔
14) √81 = 9 → 9×9=81 ✔
15) √144 = 12 → 12×12=144 ✔
16) √1600 = 40 → 40×40=1600 ✔
17) √8100 = 90 → 90×90=8100 ✔
18) √49 = 7 → 7×7=49 ✔
19) √121 = 11 → 11×11=121 ✔
20) √(-64) → Negative → IMPOSSIBLE ✔

✔ All checked.

---

Part C: Cube Roots

Cube root asks: “What number multiplied by itself three times gives this?”
Unlike square roots, cube roots CAN be negative — because a negative times itself three times stays negative.

21) ³√8 = 2 → 2×2×2=8 ✔
22) ³√27 = 3 → 3×3×3=27 ✔
23) ³√125 = 5 → 5×5×5=125 ✔
24) ³√1000 = 10 → 10×10×10=1000 ✔
25) ³√(-512) = -8 → (-8)×(-8)×(-8) = 64 × (-8) = -512 ✔
26) ³√(-125) = -5 → (-5)×(-5)×(-5) = 25 × (-5) = -125 ✔
27) ³√64 = 4 → 4×4×4=64 ✔
28) ³√343 = 7 → 7×7×7=343 ✔
29) ³√729 = 9 → 9×9×9=729 ✔
30) ³√216 = 6 → 6×6×6=216 ✔

✔ All checked.

---

Final Answer:

A1) 16
A2) -9
A3) 64
A4) 25
A5) 1000
A6) 144
A7) -512
A8) 49

B11) 4
B12) 5
B13) IMPOSSIBLE
B14) 9
B15) 12
B16) 40
B17) 90
B18) 7
B19) 11
B20) IMPOSSIBLE

C21) 2
C22) 3
C23) 5
C24) 10
C25) -8
C26) -5
C27) 4
C28) 7
C29) 9
C30) 6