化简 \sqrt[4]{(-4r^2s^6)}^2

解答

化简

4 (- 4 r^{2} s^{6})^{2}

2 r s^{3} i

求解步骤

(4 - 4 r^{2} s^{6})^{2}

使用法则:

(- a) = - a

(- 4 r^{2} s^{6}) = - 4 r^{2} s^{6}

= (4 - 4 r^{2} s^{6})^{2}

化简

4 - 4 r^{2} s^{6} : 4 2^{2} 4 r^{2} s 4 - s^{2}

= (4 2^{2} 4 r^{2} s 4 - s^{2})^{2}

使用指数法则:

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

(4 2^{2} 4 r^{2} s 4 - s^{2})^{2} = (4 2^{2})^{2} (4 r^{2})^{2} s^{2} (4 - s^{2})^{2}

= (4 2^{2})^{2} (4 r^{2})^{2} s^{2} (4 - s^{2})^{2}

使用指数法则:

a^{m} b^{m} = (ab)^{m},

假定

a \geq 0, b \geq 0

s^{2} (4 r^{2})^{2} (4 - s^{2})^{2} = (s 4 r^{2} 4 - s^{2})^{2}

= (4 2^{2})^{2} (s 4 r^{2} 4 - s^{2})^{2}

4 - s^{2} = 4 - 1 4 s^{2}

= (4 2^{2})^{2} (4 - 1 s 4 r^{2} 4 s^{2})^{2}

(4 2^{2})^{2} = 2

= 2 (4 - 1 s 4 r^{2} 4 s^{2})^{2}

(4 - 1 s 4 r^{2} 4 s^{2})^{2} = i r s^{3}

= 2 i r s^{3}

Rewrite in standard complex form:

2 r s^{3} i

= 2 r s^{3} i

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