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Simplify. Assume all variables are positive.\newlinet52t32t^{\frac{5}{2}} \cdot t^{\frac{3}{2}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______

Full solution

Q. Simplify. Assume all variables are positive.\newlinet52t32t^{\frac{5}{2}} \cdot t^{\frac{3}{2}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
  1. Identify and Apply Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinet52×t32=t(52+32)t^{\frac{5}{2}} \times t^{\frac{3}{2}} = t^{\left(\frac{5}{2} + \frac{3}{2}\right)}.
  2. Perform Exponent Addition: Perform the addition of the exponents. (52)+(32)=82(\frac{5}{2}) + (\frac{3}{2}) = \frac{8}{2}.
  3. Simplify Exponent: Simplify the exponent. 82=4\frac{8}{2} = 4.
  4. Write Final Answer: Write the final answer using the simplified exponent. t82=t4t^{\frac{8}{2}} = t^4.

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