Question

Describe a strategy for rewriting an expression as a single power.

Answer 1

To rewrite an expression as a single power, follow these steps:

1. Combine like terms: Simplify the expression by combining any like terms. For example, if the expression is 3x^2 + 2x^2, combine the x^2 terms to get 5x^2.

2. Use the properties of exponents: If the expression has multiple terms with the same base, you can use the properties of exponents to rewrite it as a single power. For example, if the expression is 2x^3 + 4x^3, you can simplify it to 6x^3.

3. Factor out common factors: If there are common factors in the terms of the expression, factor them out to rewrite the expression as a single power. For example, if the expression is 2x^2 + 6x, you can factor out 2x to get 2x(x + 3).

4. Raise the common base to the sum of the exponents: If the terms in the expression have the same base, raise the base to the sum of the exponents to rewrite the expression as a single power. For example, if the expression is x^2 * x^3, you can rewrite it as x^5.

By following these steps, you can rewrite an expression as a single power to simplify it and make it easier to work with.