Question

Using the Product Rule of Exponents, what is the exponent of 7 power of 2⋅7 power of 3 in exponential simplest form? (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The Product Rule of Exponents states that when you multiply two powers with the same base, you add their exponents.

The exponent of (7^2) * (7^3) can be found by adding the exponents:
2 + 3 = 5

So, the exponent of (7^2) * (7^3) is 5.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The Product Rule of Exponents states that when multiplying two numbers with the same base, you can keep the base and add the exponents.

In this case, we have 2 raised to the power of 7 multiplied by 7 raised to the power of 3.

Using the Product Rule of Exponents, we can simplify this as follows:

2^7 * 7^3

The base is the same, which is 7, so we can add the exponents:

2^7 * 7^(3+1)

Simplifying further, we have:

2^7 * 7^4

And finally, in exponential simplest form:

7^4 * 2^7

Answer 3

[AI-generated answer — Explain Bot]

To find the exponent of \(7^2 \cdot 7^3\) using the Product Rule of Exponents, we need to add the exponents together.

The Product Rule states that \(a^m \cdot a^n = a^{m + n}\), where \(a\) is the base and \(m\) and \(n\) are the exponents.

In this case, the base is 7 and the exponents are 2 and 3. Therefore, we have \(7^2 \cdot 7^3 = 7^{2 + 3}\).

Simplifying the exponents, we have \(7^{2 + 3} = 7^5\).

So, the exponent of \(7^2 \cdot 7^3\) in exponential simplest form is 5.