What is sqrt(5)*9*\sqrt[3]{sqrt(\sqrt{5^6)}} ?

The solution to sqrt(5)*9*\sqrt[3]{sqrt(\sqrt{5^6)}} is 45

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simplify sqrt(5)9\sqrt[3]{sqrt(\sqrt{5^6)}}

simplify

45

Solution steps

= 5 \cdot 9 \cdot 5^{\frac{1}{2}}

Apply radical rule:

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

5 = 5^{\frac{1}{2}}

= 5^{\frac{1}{2}} \cdot 9 \cdot 5^{\frac{1}{2}}

Apply exponent rule:

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

5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2}}

= 5^{\frac{1}{2} + \frac{1}{2}} \cdot 9

\frac{1}{2} + \frac{1}{2} = 1

= 5^{1} \cdot 9

Apply exponent rule:

a^{1} = a

5^{1} = 5

= 5 \cdot 9

Multiply the numbers:

5 \cdot 9 = 45

= 45

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What is sqrt(5)*9*\sqrt[3]{sqrt(\sqrt{5^6)}} ?
The solution to sqrt(5)*9*\sqrt[3]{sqrt(\sqrt{5^6)}} is 45