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Find the cube root of 512 by prime factorisation
To do: Find the cube root of 512 by prime factorization.
Solution:
Prime factors of $512 =2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
Prime factorization of $512 = 2^9$
cube root of $512 = (512)^{\frac{1}{3}} = ( 2^9 )^{\frac{1}{3}}$
$(a^m )^n = a^{m\times n}$
$( 2^9 )^{\frac{1}{3}} = ( 2 )^{9\frac{1}{3}}$
=$ 2^ 3$
= 8
Therefore the Cube root of 512 is 8
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