Question

Simplify Rewrite the expression in the form xⁿ.
x² . x⁻¹² =

Answer 1

To simplify the expression x² . x⁻¹², apply the rule of exponents by adding the exponents together, resulting in x raised to the power of -10 (x⁻¹°).

Step-by-step explanation:

The student's question: Simplify Rewrite the expression in the form xⁿ. x² . x⁻¹² =, involves the rules of exponents, specifically the product rule.

The product rule states that when you're multiplying two expressions with the same base, you add the exponents.

Here, we have x raised to the power of 2 (x²) and x raised to the power of -12 (x⁻¹²).

Using the product rule:

• Add the exponents: 2 + (-12) = -10.
• The simplified expression is x raised to the power of -10 (x⁻¹°).

This is much simpler than having to deal with the expression in a quadratic equation or completing the square, as seen in some polynomial simplifications.