Simplify cube root of 27^2

Problem

√(3,27^2)

Solution

1. Rewrite the expression using the property of exponents where √(n,a^m)=a^m/n

√(3,27^2)=27^2/3

2. Express the base 27 as a power of 3 because 3×3×3=27

27=3^3

3. Substitute the power back into the expression.

(3^3)^2/3

4. Apply the power of a power rule, which states (a^b)^c=a^(b⋅c)

3^(3⋅2/3)

5. Simplify the exponent by multiplying the fractions.

3⋅2/3=2

6. Evaluate the resulting power.

3^2=9

Final Answer

√(3,27^2)=9

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