Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Fully simplify using only positive exponents.

(24x^(3)y^(5))/(16x^(8)y^(8))
Answer:

Fully simplify using only positive exponents.\newline24x3y516x8y8 \frac{24 x^{3} y^{5}}{16 x^{8} y^{8}} \newlineAnswer:

Full solution

Q. Fully simplify using only positive exponents.\newline24x3y516x8y8 \frac{24 x^{3} y^{5}}{16 x^{8} y^{8}} \newlineAnswer:
  1. Factor and Simplify: Write down the expression and factor both the numerator and the denominator.\newline(24x3y5)/(16x8y8)(24x^{3}y^{5})/(16x^{8}y^{8}) can be factored as (83x3y5)/(82x8y8)(8 \cdot 3 \cdot x^{3} \cdot y^{5}) / (8 \cdot 2 \cdot x^{8} \cdot y^{8}).
  2. Simplify Coefficients: Simplify the coefficients by dividing 2424 by 1616. 2416\frac{24}{16} simplifies to 32\frac{3}{2} since both 2424 and 1616 are divisible by 88.
  3. Apply Quotient Rule: Apply the quotient rule for exponents to simplify x3/x8x^{3}/x^{8} and y5/y8y^{5}/y^{8}. x3/x8x^{3}/x^{8} simplifies to x5x^{-5} and y5/y8y^{5}/y^{8} simplifies to y3y^{-3}, but we want only positive exponents.
  4. Convert Negative Exponents: Convert negative exponents to positive exponents. x5x^{-5} becomes 1x5\frac{1}{x^{5}} and y3y^{-3} becomes 1y3\frac{1}{y^{3}}.
  5. Combine Coefficients and Exponents: Combine the simplified coefficients and the positive exponents. The expression now reads (32)×(1x5)×(1y3)(\frac{3}{2}) \times (\frac{1}{x^{5}}) \times (\frac{1}{y^{3}}).
  6. Write Final Expression: Write the final simplified expression.\newlineThe fully simplified expression using only positive exponents is (32)×(1x5×1y3)(\frac{3}{2}) \times (\frac{1}{x^{5}} \times \frac{1}{y^{3}}) or (32)×(1x5y3)(\frac{3}{2}) \times (\frac{1}{{x^{5}y^{3}}}).

More problems from Simplify variable expressions using properties