Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive.\newlinev54v94v^{\frac{5}{4}} \cdot v^{\frac{9}{4}}\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.\newlinev54v94v^{\frac{5}{4}} \cdot v^{\frac{9}{4}}\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 Exponent 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}.\newlinev54×v94=v54+94v^{\frac{5}{4}} \times v^{\frac{9}{4}} = v^{\frac{5}{4} + \frac{9}{4}}.
  2. Add Exponents: Add the exponents. 54+94=144.\frac{5}{4} + \frac{9}{4} = \frac{14}{4}.
  3. Simplify Exponent: Simplify the exponent. \newline144\frac{14}{4} can be simplified to 3.53.5 or 72\frac{7}{2}.\newlinev144=v72v^{\frac{14}{4}} = v^{\frac{7}{2}}.
  4. Write Final Answer: Write the final 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.\newlineThe final answer is v72v^{\frac{7}{2}}.

More problems from Simplify expressions involving rational exponents