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What is the simplified value of the exponential expression 27^1/3

User Nauer
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1 Answer

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Answer: ≈3(Although this is an estimate, there is a 50,000 character limit on these answers, so it isn't possible to put the whole number.

Step-by-step explanation:

Step 1: Determine the prime factorization of 27.

27 = 3 x 3 x 3

Step 2: Rewrite the expression using the prime factorization.

27^(1/3) = (3 x 3 x 3)^(1/3)

Step 3: Apply the exponent rule for a product raised to a power.

(3 x 3 x 3)^(1/3) = 3^(1/3) x 3^(1/3) x 3^(1/3)

Step 4: Simplify each factor.

3^(1/3) represents the cube root of 3. Since the exponent is 1/3, we are looking for the number that, when raised to the power of 3, gives us 3. The cube root of 3 is approximately 1.4422.

Step 5: Multiply the simplified factors.

3^(1/3) x 3^(1/3) x 3^(1/3) = 1.4422 x 1.4422 x 1.4422 ≈ 3

User Yaqoob
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