Simplify t · t^3. Express your answer as a single term, without a denominator.
Understand the Problem
The question is asking to simplify the expression involving exponents, specifically t multiplied by t raised to the power of 3, and to express the final answer as a single term without a denominator.
Answer
The simplified expression is \( t^4 \).
Answer for screen readers
The simplified expression is ( t^4 ).
Steps to Solve
- Identify the expression to simplify
The given expression is ( t \cdot t^3 ).
- Apply the multiplication rule for exponents
When multiplying two terms with the same base, you can add the exponents. Here, the base is ( t ), and the exponents are ( 1 ) (for ( t )) and ( 3 ) (for ( t^3 )).
This can be expressed as: $$ t^1 \cdot t^3 = t^{1+3} $$
- Simplify the exponents
Now, add the exponents: $$ t^{1+3} = t^{4} $$
- Write the final simplified expression
Thus, the simplified expression is: $$ t^4 $$
The simplified expression is ( t^4 ).
More Information
This simplification uses the multiplication rule of exponents, which states that ( a^m \cdot a^n = a^{m+n} ) for any base ( a ) and exponents ( m ) and ( n ).
Tips
- Failing to recognize that the base must be the same when adding exponents; this is crucial for applying the multiplication rule properly.
- Confusing addition of exponents with multiplication of bases.
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