How do you multiply ${\sqrt{5}}^{6}$ $sqrt5^6$ ?

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How do you multiply ${\sqrt{5}}^{6}$ $sqrt5^6$ ?

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Answer 1 · 2015-09-25T13:11:45

It is 125

Explanation:

You can calculate this in (at least) 2 ways:

1) ${\sqrt{5}}^{6} = (\sqrt{5} \sqrt{5}) (\sqrt{5} \sqrt{5}) (\sqrt{5} \sqrt{5}) = 5 \cdot 5 \cdot 5 = 125$ $sqrt(5)^6=(sqrt(5)sqrt(5))(sqrt(5)sqrt(5))(sqrt(5)sqrt(5))=5*5*5=125$

2)
You can use the laws of power operations

Write $\sqrt{5}$ $sqrt(5)$ as $5^{\frac{1}{2}}$ $5^(1/2)$ to get: ${\sqrt{5}}^{6} = {(5^{\frac{1}{2}})}^{6}$ $sqrt(5)^6=(5^(1/2))^6$
Use the law that: ${(a^{b})}^{c} = a^{b \cdot c}$ $(a^b)^c=a^(b*c)$ to get:
${(5^{\frac{1}{2}})}^{6} = 5^{\frac{1}{2} \cdot 6} = 5^{3} = 125$ $(5^(1/2))^6=5^(1/2*6)=5^3=125$

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How do you multiply ${\sqrt{5}}^{6}$ $sqrt5^6$ ?

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