Which expression is correctly developed to use the Product Rule of Exponents?(1 point)

Question

Responses

6 to the 2⋅7 to the 3rd power

10 to the 8th power ⋅10 to the 8th power

(5 to the 2nd power)9th power

32 to the 7th power

Answer 1

The expression that is correctly developed to use the Product Rule of Exponents is:

\((5^{2})^{9}\)

This is because the Product Rule of Exponents states that when you raise a power to a power, you multiply the exponents. In this case, you would calculate it as \(5^{2 \cdot 9} = 5^{18}\).

The Product Rule itself generally refers to the rule that states when multiplying two powers with the same base, you add the exponents, for example: \(a^{m} \cdot a^{n} = a^{m+n}\).

However, the expression \((5^{2})^{9}\) correctly relates to the rules of exponentiation. In contrast, the other expressions either do not require the Product Rule or aren't correctly using it.