Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expression is equivalent to (27)6(2^7)^6?\newlineChoices:\newline(A) 1242\frac{1}{2^{42}}\newline(B) 2422^{42}\newline(C) 2132^{13}\newline(D) 1213\frac{1}{2^{13}}

Full solution

Q. Which expression is equivalent to (27)6(2^7)^6?\newlineChoices:\newline(A) 1242\frac{1}{2^{42}}\newline(B) 2422^{42}\newline(C) 2132^{13}\newline(D) 1213\frac{1}{2^{13}}
  1. Understand Exponent Rule: Understand the exponent rule for powers raised to powers.\newlineWhen a power is raised to another power, we multiply the exponents.\newline(27)6=2(7×6)(2^7)^6 = 2^{(7\times6)}
  2. Calculate New Exponent: Calculate the new exponent.\newlineMultiply the exponents 77 and 66 to find the equivalent expression.\newline2(76)=2422^{(7*6)} = 2^{42}
  3. Match Result with Choices: Match the result with the given choices.\newlineThe calculation from Step 22 gives us 2422^{42}, which corresponds to choice (B).