Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive.\newlinev54v74v^{\frac{5}{4}} \cdot v^{\frac{7}{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.\newlinev54v74v^{\frac{5}{4}} \cdot v^{\frac{7}{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 Equation: 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×v74=v54+74v^{\frac{5}{4}} \times v^{\frac{7}{4}} = v^{\frac{5}{4} + \frac{7}{4}}.
  2. Add Exponents: Add the exponents. 54+74=(5+7)/4=124.\frac{5}{4} + \frac{7}{4} = \left(5 + 7\right) / 4 = \frac{12}{4}.
  3. Simplify Fraction: Simplify the fraction 124\frac{12}{4}. 124=3\frac{12}{4} = 3.
  4. Write Final Answer: Write the final answer using the simplified exponent. v54×v74=v3v^{\frac{5}{4}} \times v^{\frac{7}{4}} = v^3.

More problems from Simplify expressions involving rational exponents