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Popular >

simplify sqrt(18^x)

Solution

simplify

1 8^{x}

Solution

(32)^{x}

Solution steps

1 8^{x}

Apply radical rule:

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

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

Apply exponent rule:

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

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

Simplify

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

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

Prime factorization of

18 : 2 \cdot 3^{2}

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

Apply radical rule:

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

Apply radical rule:

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

Apply radical rule:

3^{2} = 3

= (32)^{x}

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Frequently Asked Questions (FAQ)

What is sqrt(18^x) ?
The solution to sqrt(18^x) is (3sqrt(2))^x