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Popular >

simplify sqrt(4^{3x)}

Solution

simplify

4^{3 x}

Solution

8^{x}

Solution steps

4^{3 x}

Apply radical rule:

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

= (4^{3 x})^{\frac{1}{2}}

Apply exponent rule:

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

= 4^{3 x \frac{1}{2}}

Simplify

3 x \frac{1}{2} : \frac{3 x}{2}

= 4^{\frac{3 x}{2}}

Factor the number:

4 = 2^{2}

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

Apply exponent rule:

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

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

= 2^{3 x}

Apply exponent rule:

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

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

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

2^{3} = 8

= 8^{x}

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Frequently Asked Questions (FAQ)

What is sqrt(4^{3x)} ?
The solution to sqrt(4^{3x)} is 8^x