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Popular >

simplify (6sqrt(2))^5

Solution

simplify

(62)^{5}

Solution

311042

+1

Decimal Notation

43987.69864 \dots

Solution steps

(62)^{5}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(62)^{5} = 6^{5} (2)^{5}

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

6^{5} = 7776

= 7776 (2)^{5}

(2)^{5} = 2^{2} 2

= 2^{2} \cdot 77762

Factor integer

7776 = 2^{5} \cdot 243

= 2^{5} \cdot 243 \cdot 2^{2} 2

Apply exponent rule:

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

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

= 243 \cdot 2^{5 + 2} 2

Add the numbers:

5 + 2 = 7

= 243 \cdot 2^{7} 2

2^{7} = 128

= 243 \cdot 1282

Multiply the numbers:

243 \cdot 128 = 31104

= 311042

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Frequently Asked Questions (FAQ)

What is (6sqrt(2))^5 ?
The solution to (6sqrt(2))^5 is 31104sqrt(2)