Applying the product rule of exponents, each product of powers are matched with its simplified expression as:
1. [tex]5 \times 5^3 = 5^4[/tex]
2. [tex]5 \times 5^3 = 5^4[/tex]
3. [tex]5^{-3} \times 5^{-3} = \frac{1}{5^6}[/tex]
4. [tex]5^{-4} \times 5^{4} \times 5^0 = 5^0[/tex]
5. [tex]5^{7} \times 5^{3} = 5^{10}[/tex]
To multiply the powers having the same base, we will apply the product rule for exponents.
What is the Product Rule for Exponents?
- Base on the product rule for exponents, we have, [tex]a^m \times a^n = a^{m + n} = a^{mn}[/tex].
- In order to find the products of two given numbers that have the same base, the exponents would be added together.
1. [tex]5^6 \times 5^{-4[/tex]
Add the exponents together
[tex]5^6 \times 5^{-4} = 5^{(6) + (-4)}[/tex]
[tex]5^6 \times 5^{-4} = 5^2[/tex]
2. [tex]5 \times 5^3[/tex]
Add the exponents together
[tex]5 \times 5^3 = 5^{(1 + 3)}[/tex]
[tex]5 \times 5^3 = 5^4[/tex]
3. [tex]5^{-3} \times 5^{-3}[/tex]
Add the exponents together
[tex]5^{-3} \times 5^{-3} = 5^{(-3) + (-3)[/tex]
[tex]5^{-3} \times 5^{-3} = 5^{-6[/tex]
[tex]5^{-3} \times 5^{-3} = \frac{1}{5^6}[/tex]
4. [tex]5^{-4} \times 5^{4} \times 5^0[/tex]
Add the exponents together
[tex]5^{-4} \times 5^{4} \times 5^0 = 5^{(-4) + (4) + (0)[/tex]
[tex]5^{-4} \times 5^{4} \times 5^0 = 5^0[/tex]
5. [tex]5^{7} \times 5^{3}[/tex]
Add the exponents together
[tex]5^{7} \times 5^{3} = 5^{10}[/tex]
In summary, applying the product rule of exponents, each product of powers are matched with its simplified expression as:
1. [tex]5 \times 5^3 = 5^4[/tex]
2. [tex]5 \times 5^3 = 5^4[/tex]
3. [tex]5^{-3} \times 5^{-3} = \frac{1}{5^6}[/tex]
4. [tex]5^{-4} \times 5^{4} \times 5^0 = 5^0[/tex]
5. [tex]5^{7} \times 5^{3} = 5^{10}[/tex]
Learn more about product rule of exponents on:
https://brainly.com/question/847241
