Math Problem Statement

Simplify. Rewrite the expression in the form (9^{-3})(9^{12})=

Solution

To simplify the expression (93)(912)(9^{-3})(9^{12}), we can use the property of exponents that states aman=am+na^m \cdot a^n = a^{m+n}.

  1. Apply the property: 93912=93+12=999^{-3} \cdot 9^{12} = 9^{-3 + 12} = 9^{9}

Thus, (93)(912)=99(9^{-3})(9^{12}) = 9^{9}.

If you have any questions or need further details, feel free to ask! Here are some related questions:

  1. What is the numerical value of 999^9?
  2. Can you explain the properties of exponents in more detail?
  3. How would you express 999^{9} in terms of base 3?
  4. What are some applications of exponent rules in algebra?
  5. Can you simplify a similar expression using different bases?

Tip: When multiplying terms with the same base, always add the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

a^m * a^n = a^{m+n}

Theorems

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Suitable Grade Level

Grades 6-8