Simplify t * t^(-3).
Understand the Problem
The question is asking us to simplify the expression t * t^(-3). This involves applying the laws of exponents to combine the terms effectively.
Answer
The simplified expression is \( \frac{1}{t^2} \).
Answer for screen readers
The simplified expression is ( \frac{1}{t^2} ).
Steps to Solve
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Identify the expression We start with the expression ( t \cdot t^{-3} ).
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Apply the Laws of Exponents Using the property of exponents that states ( a^m \cdot a^n = a^{m+n} ), we combine the terms. Here, ( m = 1 ) and ( n = -3 ).
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Combine the exponents Thus, we have: $$ t \cdot t^{-3} = t^{1 + (-3)} = t^{-2} $$
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Rewrite the expression The expression ( t^{-2} ) can be rewritten using the definition of negative exponents: $$ t^{-2} = \frac{1}{t^2} $$
The simplified expression is ( \frac{1}{t^2} ).
More Information
When simplifying expressions with exponents, it's essential to remember that a negative exponent indicates a reciprocal. So, ( t^{-2} ) means one over ( t^2 ).
Tips
One common mistake is forgetting to apply the exponent rule correctly, especially with negative exponents. Ensure to combine the exponents accurately and recognize the meaning of negative exponents.
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