化简 4.9((0.5^2)/(4.05^2))

解答

化简

4.9 (\frac{0. 5 ^{2}}{4.0 5 ^{2}})

0.07468 \dots

求解步骤

4.9 (\frac{0. 5 ^{2}}{4.0 5 ^{2}})

使用指数法则:

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

\frac{0. 5 ^{2}}{4.0 5 ^{2}} = (\frac{0.5}{4.05})^{2}

= 4.9 (\frac{0.5}{4.05})^{2}

(\frac{0.5}{4.05})^{2} = \frac{0. 5 ^{2}}{4.0 5 ^{2}}

= 4.9 \cdot \frac{0. 5 ^{2}}{4.0 5 ^{2}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{0. 5 ^{2} \cdot 4.9}{4.0 5 ^{2}}

0. 5^{2} \cdot 4.9 = 1.225

= \frac{1.225}{4.0 5 ^{2}}

4.0 5^{2} = 16.4025

= \frac{1.225}{16.4025}

数字相除:

\frac{1.225}{16.4025} = 0.07468 \dots

= 0.07468 \dots

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