展开 [(1/2)^2*(3/5)^2]^2

解答

展开

[(\frac{1}{2})^{2} \cdot (\frac{3}{5})^{2}]^{2}

\frac{81}{10000}

十进制

0.0081

求解步骤

((\frac{1}{2})^{2} (\frac{3}{5})^{2})^{2}

化简

(\frac{1}{2})^{2} (\frac{3}{5})^{2} : (\frac{3}{10})^{2}

= ((\frac{3}{10})^{2})^{2}

(\frac{3}{10})^{2} = \frac{3 ^{2}}{1 0 ^{2}}

= (\frac{3 ^{2}}{1 0 ^{2}})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 ^{2} ) ^{2}}{( 1 0 ^{2} ) ^{2}}

(1 0^{2})^{2} : 1 0^{4}

= \frac{( 3 ^{2} ) ^{2}}{1 0 ^{4}}

(3^{2})^{2} : 3^{4}

= \frac{3 ^{4}}{1 0 ^{4}}

3^{4} = 81

= \frac{81}{1 0 ^{4}}

1 0^{4} = 10000

= \frac{81}{10000}

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