Final answer:
The expression a⁵ x a⁴/a² simplifies to a⁷ using the laws of exponents. We add the exponents when multiplying the same bases and subtract the exponent when dividing, leading to the correct answer option C) a⁷.
Step-by-step explanation:
The question asks us to simplify the expression a⁵ x a⁴/a².
This involves the laws of exponents, specifically the quotient rule, (xʳ)/x^b = x^(a-b), and the product rule, (x^a)(x^b) = x^(a+b).
Applying these rules, we multiply the exponents in the numerator and subtract the exponent in the denominator:
a⁵ x a⁴ = a^(5+4) = a⁹
And then we divide by a²: a⁹/a²
= a^(9-2)
= a⁷
Therefore, the simplified form of the expression is a⁷, which matches option C).