Math Problem Statement

Simplify. Express your answer using positive exponents. 4ab9a9b9

Solution

To simplify the expression 4ab9a9b94ab^9a^9b^9 and express it using positive exponents:

  1. First, group the like terms together: 4aa9b9b94a \cdot a^9 \cdot b^9 \cdot b^9

  2. Next, apply the rule of exponents xmxn=xm+nx^m \cdot x^n = x^{m+n} to combine the like terms: 4a1+9b9+94 \cdot a^{1+9} \cdot b^{9+9}

  3. Simplify the exponents: 4a10b184a^{10}b^{18}

So, the simplified expression is 4a10b18\boxed{4a^{10}b^{18}}.

Would you like more details on the steps? Here are some related questions:

  1. What are the basic rules of exponents?
  2. How can you simplify expressions with multiple variables?
  3. What is the importance of expressing answers with positive exponents?
  4. Can you provide an example where exponents are negative?
  5. How would you simplify an expression with fractional exponents?

Tip: Remember, when multiplying terms with the same base, you add their exponents.

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Monomials

Formulas

Exponent Rules

Theorems

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Suitable Grade Level

Grades 7-9