Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select all the expressions that are equivalent to 38×333^{-8} \times 3^{-3}.\newlineMulti-select Choices:\newline(A) 3113^{-11}\newline(B) 3243^{24}\newline(C) 3833\frac{3^{-8}}{3^{3}}\newline(D) 1311\frac{1}{3^{-11}}

Full solution

Q. Select all the expressions that are equivalent to 38×333^{-8} \times 3^{-3}.\newlineMulti-select Choices:\newline(A) 3113^{-11}\newline(B) 3243^{24}\newline(C) 3833\frac{3^{-8}}{3^{3}}\newline(D) 1311\frac{1}{3^{-11}}
  1. Calculate Exponents: Step 11: Calculate the product of 383^{-8} and 333^{-3}.\newlineWhen multiplying powers with the same base, add the exponents.\newline38×33=3(8+(3))=3113^{-8} \times 3^{-3} = 3^{(-8 + (-3))} = 3^{-11}
  2. Compare with Choices: Step 22: Compare the result with the given choices.\newline(A) 3113^{-11} matches our calculation.\newline(B) 3243^{24} is not equivalent because it has a positive exponent and is a product, not a quotient.\newline(C) 3833\frac{3^{-8}}{3^{3}} simplifies to 3113^{-11}, which matches our calculation.\newline(D) 1311\frac{1}{3^{-11}} simplifies to 3113^{11}, which is not equivalent because it has a positive exponent.

More problems from Simplify exponential expressions using exponent rules