Question

How can the following expression be simplified and written without negative exponents? a⁻⁷.a¹2/a⁻⁵

a) a¹⁰
b) a¹⁴
c) a⁻⁴
d) a⁻¹⁰

Answer 1

The simplified form of the expression a⁻⁷.a¹²/a⁻⁵ is a¹⁰ after applying the properties of exponents to add and subtract exponents with the same base. The correct answer is (a) a¹⁰.

Step-by-step explanation:

The expression a⁻⁷.a¹²/a⁻⁵ can be simplified using the properties of exponents. When multiplying expressions with the same base, we add the exponents, and when dividing, we subtract the exponents. Here's a step-by-step simplification:

• Combine the exponents from the numerator: a⁻⁷ × a¹² = a⁻⁷ + ¹² = a⁻⁷ + 12 = a⁵.
• Subtract the exponent in the denominator from the result: a⁵ / a⁻⁵ = a⁵ - (⁻⁵) = a⁵ + 5 = a¹⁰.

Thus, the expression simplifies to a¹⁰, which does not have any negative exponents. The correct answer is (a) a¹⁰.