What is sqrt(8^{(x-1))} ?

The solution to sqrt(8^{(x-1))} is (2sqrt(2))^{x-1}

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simplify sqrt(8^{(x-1))}

simplify

8^{(x - 1)}

(22)^{x - 1}

Solution steps

8^{(x - 1)}

Apply radical rule:

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

= (8^{x - 1})^{\frac{1}{2}}

Apply exponent rule:

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

= 8^{(x - 1) \frac{1}{2}}

Simplify

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

= 8^{\frac{x - 1}{2}}

Prime factorization of

8 : 2^{3}

= (2^{3})^{\frac{x - 1}{2}}

Apply radical rule:

= (2^{3})^{x - 1}

Apply exponent rule:

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

= (2 \cdot 2^{2})^{x - 1}

Apply radical rule:

= (2 2^{2})^{x - 1}

Apply radical rule:

2^{2} = 2

= (22)^{x - 1}

(2 x x + y) (2 x + y)

(x + y)^{2} x^{2} y

\frac{x - 1}{2 x + 3}

e^{3 x} \cdot e^{6}

8 x \cdot 3 x