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Alexxx [7]
2 years ago
10

Multiplying Powers with the Same Base

Mathematics
1 answer:
Luda [366]2 years ago
5 0

Applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. 5 \times 5^3 = 5^4

2. 5 \times 5^3 = 5^4

3. 5^{-3} \times 5^{-3} = \frac{1}{5^6}

4. 5^{-4} \times 5^{4} \times 5^0 = 5^0

5. 5^{7} \times 5^{3} = 5^{10}

To multiply the powers having the same base, we will apply the product rule for exponents.

<h3>What is the Product Rule for Exponents?</h3>
  • Base on the product rule for exponents, we have, a^m \times a^n = a^{m + n} = a^{mn}.
  • In order to find the products of two given numbers that have the same base, the exponents would be added together.

1. 5^6 \times 5^{-4

Add the exponents together

5^6 \times 5^{-4} = 5^{(6) + (-4)}

5^6 \times 5^{-4} = 5^2

2. 5 \times 5^3

Add the exponents together

5 \times 5^3 = 5^{(1 + 3)}

5 \times 5^3 = 5^4

3. 5^{-3} \times 5^{-3}

Add the exponents together

5^{-3} \times 5^{-3} = 5^{(-3) + (-3)

5^{-3} \times 5^{-3} = 5^{-6

5^{-3} \times 5^{-3} = \frac{1}{5^6}

4. 5^{-4} \times 5^{4} \times 5^0

Add the exponents together

5^{-4} \times 5^{4} \times 5^0 = 5^{(-4) + (4) + (0)

5^{-4} \times 5^{4} \times 5^0 = 5^0

5. 5^{7} \times 5^{3}

Add the exponents together

5^{7} \times 5^{3} = 5^{10}

In summary, applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. 5 \times 5^3 = 5^4

2. 5 \times 5^3 = 5^4

3. 5^{-3} \times 5^{-3} = \frac{1}{5^6}

4. 5^{-4} \times 5^{4} \times 5^0 = 5^0

5. 5^{7} \times 5^{3} = 5^{10}

Learn more about product rule of exponents on:

brainly.com/question/847241

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