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Popular >

simplify sqrt(8^x)

Solution

simplify

8^{x}

Solution

(22)^{x}

Solution steps

8^{x}

Apply radical rule:

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

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

Apply exponent rule:

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

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

Simplify

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

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

Prime factorization of

8 : 2^{3}

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

Apply radical rule:

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

Apply exponent rule:

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

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

Apply radical rule:

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

Apply radical rule:

2^{2} = 2

= (22)^{x}

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Frequently Asked Questions (FAQ)

What is sqrt(8^x) ?
The solution to sqrt(8^x) is (2sqrt(2))^x