simplify 432^{1/4}

Solution

simplify

43 2^{\frac{1}{4}}

2 \cdot 3^{\frac{3}{4}}

Decimal Notation

4.55901 \dots

Solution steps

43 2^{\frac{1}{4}}

Prime factorization of

432 : 2^{4} \cdot 3^{3}

= (2^{4} \cdot 3^{3})^{\frac{1}{4}}

Apply exponent rule:

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

(2^{4} \cdot 3^{3})^{\frac{1}{4}} = (2^{4})^{\frac{1}{4}} (3^{3})^{\frac{1}{4}}

= (2^{4})^{\frac{1}{4}} (3^{3})^{\frac{1}{4}}

(2^{4})^{\frac{1}{4}} = 2

= 2 (3^{3})^{\frac{1}{4}}

Apply exponent rule:

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

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

= 2 \cdot 3^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= 2 \cdot 3^{\frac{3}{4}}

- 25 - - 96 + 16 + - 6

\frac{2 ( q ^{3} ) ^{3}}{6 q ^{10}}

(a - b) - (a + b)

(x + y) (x^{2} - 3 x y + 2 y^{2})

\frac{3 w}{4 w + 8} - \frac{w + 1}{w + 2}