Worksheet on simplifying rational exponents with handwritten answers.

Looking at the problem:
We are asked to simplify:
(27p⁶)^(2/3)

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Step 1: Understand what a rational exponent means.
The exponent 2/3 means:
→ First, take the cube root (because of the denominator 3),
→ Then, square the result (because of the numerator 2).
Or, you can think of it as: raise to the 2nd power, then take the cube root — same result.

But since we have a product inside the parentheses — 27 and p⁶ — we can apply the exponent to each part separately.

So:
(27p⁶)^(2/3) = 27^(2/3) × (p⁶)^(2/3)

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Step 2: Simplify 27^(2/3)

First, find the cube root of 27:
√³27 = 3, because 3×3×3 = 27.

Then square that result:
3² = 9

So, 27^(2/3) = 9

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Step 3: Simplify (p⁶)^(2/3)

Use the rule: (a^m)^n = a^(m×n)

So:
(p⁶)^(2/3) = p^(6 × 2/3) = p^(12/3) = p⁴

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Step 4: Multiply the simplified parts together

9 × p⁴ = 9p⁴

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Final Answer:
9p⁴