Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive.\newlineb114b54b^{\frac{11}{4}} \cdot b^{\frac{5}{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.\newlineb114b54b^{\frac{11}{4}} \cdot b^{\frac{5}{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 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: \newlinebmn×bpq=bmn+pqb^{\frac{m}{n}} \times b^{\frac{p}{q}} = b^{\frac{m}{n} + \frac{p}{q}}.
  2. Add Exponents: Add the exponents (114)(\frac{11}{4}) and (54)(\frac{5}{4}).114+54=11+54=164\frac{11}{4} + \frac{5}{4} = \frac{11 + 5}{4} = \frac{16}{4}.
  3. Simplify Fraction: Simplify the fraction 164\frac{16}{4}. 1616 divided by 44 equals 44.
  4. Write Final Answer: Write the final answer using the simplified exponent. b164=b4b^{\frac{16}{4}} = b^4.

More problems from Simplify expressions involving rational exponents