Question

What is the relationship between the exponents of the factors and
the exponent of the product in your equation?
(3^3)(3^4)

Answer 1

The relationship between the exponents of the factors and the exponents of the product in the equation is that;

The factors which are the base remain the same while the product shows that the exponents have been added to each other.

To solve this, we need to understand the rules of exponents.

We are given the equation; 3³ × 3⁴

• This involves multiplication and thus we will use use the product rule of exponents.

• The product rule of exponents states that when we multiply two exponents with the same base, the the solution is to add the exponents and retain the base.

In this our example, the base is 3 while the exponents are 3 and 4. Thus, applying the product rule of exponents, the solution is;

3³ × 3⁴ = 3⁽³ ⁺ ⁴⁾

⇒ 3⁷

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