Math Problem Statement

To simplify this​ expression, first find the base of the exponential term. Then simplify the expression. 3x^-2 The base of the exponential term is

Solution

The expression you provided is 3x23x^{-2}.

The exponential term here is x2x^{-2}. The base of the exponential term is xx, because the exponent is applied to xx.

Now, let's simplify the expression 3x23x^{-2}:

  • By the rule of exponents, xn=1xnx^{-n} = \frac{1}{x^n}, so: 3x2=3×1x2=3x23x^{-2} = 3 \times \frac{1}{x^2} = \frac{3}{x^2}

So, the simplified form of the expression is 3x2\frac{3}{x^2}.

Let me know if you'd like more details on any part of the process!

Here are 5 related questions to explore further:

  1. How do negative exponents work in general?
  2. Can you simplify the expression 2x3+4x12x^{-3} + 4x^{-1}?
  3. What happens when you have multiple negative exponents in a product like x1y2x^{-1}y^{-2}?
  4. How can you combine terms with negative exponents?
  5. What is the difference between xnx^{-n} and xn-x^n?

Tip: To simplify terms with negative exponents, always move the term with the negative exponent to the denominator and change the sign of the exponent to positive.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Algebraic Expressions

Formulas

x^{-n} = \frac{1}{x^n}

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10