化简 (0.21^2)/((pi/4 (0.91)^2)^2)

解答

化简

\frac{0.2 1 ^{2}}{( \frac{π}{4} ( 0.91 ) ^{2} ) ^{2}}

0.10425 \dots

求解步骤

\frac{0.2 1 ^{2}}{( \frac{π}{4} ( 0.91 ) ^{2} ) ^{2}}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{0.2 1 ^{2}}{( \frac{π}{4} \cdot 0.9 1 ^{2} ) ^{2}} = (\frac{0.21}{\frac{π}{4} \cdot 0.9 1 ^{2}})^{2}

= (\frac{0.21}{\frac{π}{4} \cdot 0.9 1 ^{2}})^{2}

\frac{0.21}{\frac{π}{4} \cdot 0.9 1 ^{2}} = \frac{0.21}{0.65038 \dots}

= (\frac{0.21}{0.65038 \dots})^{2}

使用指数法则:

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

= \frac{0.2 1 ^{2}}{0.65038 \dots ^{2}}

0.2 1^{2} = 0.0441

= \frac{0.0441}{0.65038 \dots ^{2}}

0.65038 \dots^{2} = 0.42300 \dots

= \frac{0.0441}{0.42300 \dots}

数字相除:

\frac{0.0441}{0.42300 \dots} = 0.10425 \dots

= 0.10425 \dots

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