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Simplify. Assume all variables are positive.\newlinet67t17t^{\frac{6}{7}} \cdot t^{\frac{1}{7}}\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.\newlinet67t17t^{\frac{6}{7}} \cdot t^{\frac{1}{7}}\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 Equation and Apply Rule: Identify the equation and apply the exponent rule 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}.\newlinet67×t17=t67+17t^{\frac{6}{7}} \times t^{\frac{1}{7}} = t^{\frac{6}{7} + \frac{1}{7}}.
  2. Add Exponents: Add the exponents.\newline67+17=6+17=77\frac{6}{7} + \frac{1}{7} = \frac{6 + 1}{7} = \frac{7}{7}.\newlinet67+17=t77t^{\frac{6}{7} + \frac{1}{7}} = t^{\frac{7}{7}}.
  3. Simplify Exponent: Simplify the exponent. t77=t1t^{\frac{7}{7}} = t^1.
  4. Recognize Power of 11: Recognize that any number to the power of 11 is the number itself. t1=tt^1 = t.

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