Math worksheet on exponents and powers with five problems.

It looks like the image you uploaded contains a worksheet on exponents and powers, but the text in question 5 is not clearly visible due to blurriness or low resolution. However, I can help solve all the problems that are readable.

Let’s go through each problem step by step:

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1. Find the multiplicative inverse of the following:

The multiplicative inverse of a number $ a $ is $ \frac{1}{a} $. For exponents, recall:
$$
a^{-n} = \frac{1}{a^n}
\Rightarrow \text{Multiplicative inverse of } a^n = a^{-n}
$$

So, the multiplicative inverse of $ a^{-n} $ is $ a^n $.

#### a) $ 3^{-4} $
- Multiplicative inverse = $ 3^4 = 81 $

#### b) $ 7^{-2} $
- Multiplicative inverse = $ 7^2 = 49 $

#### c) $ 9^{-9} $
- Multiplicative inverse = $ 9^9 $

Note: $ 9 = 3^2 $, so $ 9^9 = (3^2)^9 = 3^{18} $, but unless asked, we can leave as $ 9^9 $

#### d) $ 10^{-80} $
- Multiplicative inverse = $ 10^{80} $

✔ Answers:
- a) $ 3^4 $
- b) $ 7^2 $
- c) $ 9^9 $
- d) $ 10^{80} $

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2. Expand the following numbers using exponents

We use place value with powers of 10.

#### a) $ 18964.63 $

Break it down:
- $ 1 \times 10^4 $
- $ 8 \times 10^3 $
- $ 9 \times 10^2 $
- $ 6 \times 10^1 $
- $ 4 \times 10^0 $
- $ 6 \times 10^{-1} $
- $ 3 \times 10^{-2} $

So,
$$
18964.63 = 1 \times 10^4 + 8 \times 10^3 + 9 \times 10^2 + 6 \times 10^1 + 4 \times 10^0 + 6 \times 10^{-1} + 3 \times 10^{-2}
$$

#### b) $ 7064.373 $

- $ 7 \times 10^3 $
- $ 0 \times 10^2 $
- $ 6 \times 10^1 $
- $ 4 \times 10^0 $
- $ 3 \times 10^{-1} $
- $ 7 \times 10^{-2} $
- $ 3 \times 10^{-3} $

So,
$$
7064.373 = 7 \times 10^3 + 0 \times 10^2 + 6 \times 10^1 + 4 \times 10^0 + 3 \times 10^{-1} + 7 \times 10^{-2} + 3 \times 10^{-3}
$$

✔ Answer:
- a) $ 1 \times 10^4 + 8 \times 10^3 + 9 \times 10^2 + 6 \times 10^1 + 4 \times 10^0 + 6 \times 10^{-1} + 3 \times 10^{-2} $
- b) $ 7 \times 10^3 + 6 \times 10^1 + 4 \times 10^0 + 3 \times 10^{-1} + 7 \times 10^{-2} + 3 \times 10^{-3} $

(Note: We skip $ 0 \times 10^2 $ since it's zero.)

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3. Simplify and write in exponential form

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

#### a) $ (-3)^{-3} \times (-3)^{-2} \times (-3)^{-5} $

Same base → add exponents:
$$
(-3)^{-3 + (-2) + (-5)} = (-3)^{-10}
$$

✔ Answer: $ (-3)^{-10} $

#### b) $ a^{-8} \times a^{-10} \times a^{-2} $

Add exponents:
$$
a^{-8 + (-10) + (-2)} = a^{-20}
$$

✔ Answer: $ a^{-20} $

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4. Express $ 9^{-3} $ as a power with base 3

We know:
$$
9 = 3^2 \Rightarrow 9^{-3} = (3^2)^{-3} = 3^{2 \times (-3)} = 3^{-6}
$$

✔ Answer: $ 3^{-6} $

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5. Find the value of:

The expressions are not clearly visible in your image. They appear as blurred symbols like:

```
• [10^5 + 10^4 + 10^3]
• [10^6 + 10^5] ÷ 10^4
• [10^8 + 10^7]
• (10^2 - 10^1) × (10^2 + 10)
```

But these are not legible. However, based on common patterns, let me assume the intended questions are:

#### a) $ 10^5 + 10^4 + 10^3 $
= $ 100000 + 10000 + 1000 = 111000 $

#### b) $ (10^6 + 10^5) ÷ 10^4 $
= $ (1000000 + 100000) ÷ 10000 = 1100000 ÷ 10000 = 110 $

#### c) $ 10^8 + 10^7 $
= $ 100000000 + 10000000 = 110000000 $

#### d) $ (10^2 - 10^1) \times (10^2 + 10) $
= $ (100 - 10) \times (100 + 10) = 90 \times 110 = 9900 $

But without clear visibility, this is assumed.

If you can re-upload a clearer version of the image or type out the exact expressions for question 5, I can give you the accurate solution.

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✔ Final Answers Summary:

#### 1. Multiplicative Inverse
a) $ 3^4 $
b) $ 7^2 $
c) $ 9^9 $
d) $ 10^{80} $

#### 2. Expand using exponents
a) $ 1 \times 10^4 + 8 \times 10^3 + 9 \times 10^2 + 6 \times 10^1 + 4 \times 10^0 + 6 \times 10^{-1} + 3 \times 10^{-2} $
b) $ 7 \times 10^3 + 6 \times 10^1 + 4 \times 10^0 + 3 \times 10^{-1} + 7 \times 10^{-2} + 3 \times 10^{-3} $

#### 3. Simplify
a) $ (-3)^{-10} $
b) $ a^{-20} $

#### 4. Express $ 9^{-3} $ as power of 3
$ 3^{-6} $

#### 5. Value of (assumed):
a) $ 111000 $
b) $ 110 $
c) $ 110000000 $
d) $ 9900 $

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Please confirm or clarify question 5 if needed!