Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer using a single exponent.\newline(3a8)3(3a^8)^3

Full solution

Q. Simplify. Express your answer using a single exponent.\newline(3a8)3(3a^8)^3
  1. Apply power rule: Apply the power of a power rule to the expression (3a8)3(3a^8)^3. The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent outside the parentheses that needs to be distributed to both the coefficient 33 and the variable a8a^8. (3a8)3=33×(a8)3(3a^8)^3 = 3^3 \times (a^8)^3
  2. Calculate 333^3: Calculate 333^3.\newline333^3 is 33 multiplied by itself three times.\newline33=3×3×3=273^3 = 3 \times 3 \times 3 = 27
  3. Multiply exponents: Multiply the exponents for (a8)3(a^8)^3. According to the power of a power rule, we multiply the exponents 88 and 33. (a8)3=a(8×3)=a24(a^8)^3 = a^{(8 \times 3)} = a^{24}
  4. Combine results: Combine the results from Step 22 and Step 33.\newlineWe have calculated 333^3 to be 2727 and (a8)3(a^8)^3 to be a24a^{24}. Now we combine these results to express the simplified form of the original expression.\newline(3a8)3=27×a24(3a^8)^3 = 27 \times a^{24}