Math worksheet focusing on exponents and simplification of powers of 10 and 2.

Let's solve the problems step by step.

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Problem 1: Express as a whole number or a sum of whole numbers

We are given powers of 10 and powers of 2. Let’s compute each one:

#### Powers of 10:
- $10^0 = 1$
- $10^1 = 10$
- $10^2 = 100$
- $10^3 = 1,000$
- $10^4 = 10,000$
- $10^5 = 100,000$
- $10^6 = 1,000,000$
- $10^7 = 10,000,000$

#### Powers of 2:
- $2^0 = 1$
- $2^1 = 2$
- $2^2 = 4$
- $2^3 = 8$
- $2^4 = 16$
- $2^5 = 32$
- $2^6 = 64$
- $2^7 = 128$

So the completed table is:

| $10^0$ | $2^0$ |
|--------|-------|
| 1 | 1 |
| $10^1$ | $2^1$ |
| 10 | 2 |
| $10^2$ | $2^2$ |
| 100 | 4 |
| $10^3$ | $2^3$ |
| 1,000 | 8 |
| $10^4$ | $2^4$ |
| 10,000 | 16 |
| $10^5$ | $2^5$ |
| 100,000| 32 |
| $10^6$ | $2^6$ |
| 1,000,000| 64 |
| $10^7$ | $2^7$ |
| 10,000,000| 128 |

✔ These are all whole numbers.

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Problem 2: Simplify

We simplify expressions using exponent rules:

#### (a) $(10^2)(10^{-3})$

Use the rule: $a^m \cdot a^n = a^{m+n}$

$$
(10^2)(10^{-3}) = 10^{2 + (-3)} = 10^{-1} = \frac{1}{10} = 0.1
$$

But since the instruction says "simplify", and it may expect a fraction or decimal:

Answer: $ \boxed{0.1} $ or $ \boxed{\frac{1}{10}} $

#### (b) $(2^3)(2^{-2})$

$$
= 2^{3 + (-2)} = 2^1 = 2
$$

Answer: $ \boxed{2} $

#### (c) $(10^3)(10^{-2})$

$$
= 10^{3 - 2} = 10^1 = 10
$$

Answer: $ \boxed{10} $

#### (d) $(2^3)(2^{-1})$

$$
= 2^{3 - 1} = 2^2 = 4
$$

Answer: $ \boxed{4} $

#### (e) $(10^0)(10^4)$

$$
= 10^{0 + 4} = 10^4 = 10,000
$$

Answer: $ \boxed{10,000} $

#### (f) $(2^5)(2^{-2})$

$$
= 2^{5 - 2} = 2^3 = 8
$$

Answer: $ \boxed{8} $

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✔ Final Answers:

#### Problem 1:
| $10^0$ | $2^0$ |
|--------|-------|
| 1 | 1 |
| $10^1$ | $2^1$ |
| 10 | 2 |
| $10^2$ | $2^2$ |
| 100 | 4 |
| $10^3$ | $2^3$ |
| 1,000 | 8 |
| $10^4$ | $2^4$ |
| 10,000 | 16 |
| $10^5$ | $2^5$ |
| 100,000| 32 |
| $10^6$ | $2^6$ |
| 1,000,000| 64 |
| $10^7$ | $2^7$ |
| 10,000,000| 128 |

#### Problem 2:
1. $(10^2)(10^{-3}) = \boxed{0.1}$
2. $(2^3)(2^{-2}) = \boxed{2}$
3. $(10^3)(10^{-2}) = \boxed{10}$
4. $(2^3)(2^{-1}) = \boxed{4}$
5. $(10^0)(10^4) = \boxed{10,000}$
6. $(2^5)(2^{-2}) = \boxed{8}$

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