Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive.\newliner32r32r^{\frac{3}{2}} \cdot r^{\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.\newliner32r32r^{\frac{3}{2}} \cdot r^{\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: \newlineam×an=a(m+n)a^m \times a^n = a^{(m+n)}\newlineSo, r32×r32r^{\frac{3}{2}} \times r^{\frac{3}{2}} becomes r(32+32)r^{(\frac{3}{2} + \frac{3}{2})}.
  2. Add Exponents: Add the exponents. 32+32=62\frac{3}{2} + \frac{3}{2} = \frac{6}{2}
  3. Simplify Fraction: Simplify the fraction 62\frac{6}{2}. 62=3\frac{6}{2} = 3
  4. Write Final Answer: Write the final answer using the simplified exponent. r32+32r^{\frac{3}{2} + \frac{3}{2}} is r3r^3.

More problems from Simplify expressions involving rational exponents