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Popular >

simplify 405^{1/3}

Solution

simplify

40 5^{\frac{1}{3}}

Solution

3 \cdot 1 5^{\frac{1}{3}}

+1

Decimal Notation

7.39863 \dots

Solution steps

40 5^{\frac{1}{3}}

Prime factorization of

405 : 3^{4} \cdot 5

= (3^{4} \cdot 5)^{\frac{1}{3}}

Apply exponent rule:

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

3^{4} \cdot 5 = 3^{3} \cdot 3 \cdot 5

= (3^{3} \cdot 3 \cdot 5)^{\frac{1}{3}}

Apply exponent rule:

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

(3^{3} \cdot 3 \cdot 5)^{\frac{1}{3}} = (3^{3})^{\frac{1}{3}} (3 \cdot 5)^{\frac{1}{3}}

= (3^{3})^{\frac{1}{3}} (3 \cdot 5)^{\frac{1}{3}}

(3^{3})^{\frac{1}{3}} = 3

= 3 (3 \cdot 5)^{\frac{1}{3}}

Multiply the numbers:

3 \cdot 5 = 15

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

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Frequently Asked Questions (FAQ)

What is 405^{1/3} ?
The solution to 405^{1/3} is 3*15^{1/3}