simplify sqrt(9^x)

Solution

simplify

9^{x}

3^{x}

Solution steps

9^{x}

Apply radical rule:

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

= (9^{x})^{\frac{1}{2}}

Apply exponent rule:

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

= 9^{x \frac{1}{2}}

Simplify

x \frac{1}{2} : \frac{x}{2}

= 9^{\frac{x}{2}}

Factor the number:

9 = 3^{2}

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

Apply exponent rule:

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

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

= 3^{x}

e^{- x} \times e^{2 x}

\frac{1}{4} z e^{- ∣ z ∣}