Math Problem Statement

w-2^{\placeholder{}} $$$$ w^{-4}w^5

Solution

It looks like you’re working with an expression that involves exponents and possibly some placeholders. To clarify, here's a breakdown of the two parts:

  1. First part: 2placeholder-2^{\text{placeholder}}

    • This seems to indicate 2-2 raised to some power. If you’re aiming to substitute a specific value for the placeholder, that will determine the final expression.
  2. Second part: w4w5w^{-4}w^5

    • Using the property of exponents where aman=am+na^m \cdot a^n = a^{m+n}, this simplifies to: w4w5=w4+5=w1=ww^{-4}w^5 = w^{-4 + 5} = w^1 = w

If you're working on simplifying or solving for a particular value, let me know what the placeholder represents or if you'd like help with any specific part of the equation.

Would you like more details on how to handle exponents? Or do you have another example?

Here are some related questions for you:

  1. How do you simplify expressions involving exponents with different signs (like w4w5w^{-4}w^5)?
  2. What does the negative exponent mean in expressions like 2placeholder-2^{\text{placeholder}}?
  3. Can you apply exponent rules when dealing with negative numbers raised to exponents?
  4. How do you simplify expressions with variables in the base and constants in the exponent?
  5. How do you handle exponentiation in terms of both base and exponent being negative?

Tip: Always remember the rule aman=am+na^m \cdot a^n = a^{m+n} when combining terms with the same base.

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Math Problem Analysis

Mathematical Concepts

Exponents
Simplifying Expressions
Exponent Rules

Formulas

Exponent rule: a^m * a^n = a^(m+n)
Negative exponent rule: a^{-n} = 1/a^n

Theorems

Exponent multiplication rule

Suitable Grade Level

Grades 6-8