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Popular >

simplify sqrt(2^{n^{2.5)}}

Solution

simplify

2^{n^{2.5}}

Solution

1.41421 \dots^{n^{2.5}}

Solution steps

2^{n^{2.5}}

Apply radical rule:

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

= (2^{n^{2.5}})^{\frac{1}{2}}

Apply exponent rule:

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

= 2^{n^{2.5} \frac{1}{2}}

Simplify

n^{2.5} \frac{1}{2} : 0.5 n^{2.5}

= 2^{0.5 n^{2.5}}

Apply exponent rule:

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

2^{0.5 n^{2.5}} = (2)^{n^{2.5}}

= (2)^{n^{2.5}}

2 = 1.41421 \dots

= 1.41421 \dots^{n^{2.5}}

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Frequently Asked Questions (FAQ)

What is sqrt(2^{n^{2.5)}} ?
The solution to sqrt(2^{n^{2.5)}} is 1.41421…^{n^{2.5}}