What is sqrt(27^{x+2)} ?

The solution to sqrt(27^{x+2)} is (3sqrt(3))^{x+2}

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Popular >

simplify sqrt(27^{x+2)}

simplify

2 7^{x + 2}

(33)^{x + 2}

Solution steps

2 7^{x + 2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2 7^{x + 2})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2 7^{(x + 2) \frac{1}{2}}

Simplify

(x + 2) \frac{1}{2} : \frac{x + 2}{2}

= 2 7^{\frac{x + 2}{2}}

Prime factorization of

27 : 3^{3}

= (3^{3})^{\frac{x + 2}{2}}

Apply radical rule:

= (3^{3})^{x + 2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= (3 \cdot 3^{2})^{x + 2}

Apply radical rule:

= (3 3^{2})^{x + 2}

Apply radical rule:

3^{2} = 3

= (33)^{x + 2}

(\frac{4 e ^{4}}{3 e ^{- 2} e ^{3}})^{- 2}

2 x \cdot 5 x \cdot 3 x

e^{- 53}

e^{- 3 s}

(\frac{1}{2} a^{2}) (\frac{4}{5} a^{3} b)