Math Problem Statement

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

Solution

To simplify the expression 3x23x^{-2}, let's follow these steps:

Step 1: Identify the base of the exponential term

In the expression 3x23x^{-2}, the base of the exponential term is xx, and the exponent is 2-2.

Step 2: Apply the rule for negative exponents

The rule for negative exponents is:

an=1ana^{-n} = \frac{1}{a^n}

Using this rule, we can rewrite x2x^{-2} as:

x2=1x2x^{-2} = \frac{1}{x^2}

Step 3: Simplify the expression

Now, substitute this into the original expression:

3x2=3×1x2=3x23x^{-2} = 3 \times \frac{1}{x^2} = \frac{3}{x^2}

Final simplified expression:

3x2\frac{3}{x^2}

Would you like more details or have any questions about this simplification?

Here are some related questions for you:

  1. What happens when the exponent is a positive integer instead of negative?
  2. How do you handle fractional exponents in expressions like x12x^{\frac{1}{2}}?
  3. Can you simplify expressions with both positive and negative exponents?
  4. How would you simplify 4x34x^{-3} using the same process?
  5. What are the rules for exponents when multiplying two terms with the same base?

Tip: Remember, negative exponents are a way of representing division.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents

Formulas

a^{-n} = 1/a^n

Theorems

Exponent rules

Suitable Grade Level

Grades 7-9