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Popular >

simplify (36^{1/2})^5

Solution

simplify

(3 6^{\frac{1}{2}})^{5}

Solution

7776

Solution steps

(3 6^{\frac{1}{2}})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3 6^{\frac{1}{2} \cdot 5}

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

= 3 6^{\frac{5}{2}}

Factor the number:

36 = 6^{2}

= (6^{2})^{\frac{5}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 6^{2 \cdot \frac{5}{2}}

2 \cdot \frac{5}{2} = 5

= 6^{5}

6^{5} = 7776

= 7776

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Frequently Asked Questions (FAQ)

What is (36^{1/2})^5 ?
The solution to (36^{1/2})^5 is 7776