0.46 * 196^0.64 *196^0.64

asked by guest
on Sep 21, 2024 at 7:38 am



You asked:

Evaluate the expression: \(0.46 \cdot {196}^{0.64} \cdot {196}^{0.64}\)

MathBot Answer:

\[0.46 \cdot {196}^{0.64} \cdot {196}^{0.64} = \frac{2254 \cdot 14^{\frac{14}{25}}}{25} \approx 395.2260873974026418169778234478217\]

\[\begin{aligned}0.46 \cdot {196}^{0.64} \cdot {196}^{0.64}& = \frac{46}{100} \cdot 196^{\frac{64}{100}} \cdot 196^{\frac{64}{100}}\\& = \frac{46}{100} \cdot 196^{\frac{16}{25}} \cdot 196^{\frac{64}{100}}\\& = \frac{46}{100} \cdot 14 \cdot 14^{\frac{7}{25}} \cdot 196^{\frac{64}{100}}\\& = \frac{46}{100} \cdot 14 \cdot 14^{\frac{7}{25}} \cdot 196^{\frac{16}{25}}\\& = \frac{46}{100} \cdot 14 \cdot 14^{\frac{7}{25}} \cdot 14 \cdot 14^{\frac{7}{25}}\\& = \frac{23}{50} \cdot 14 \cdot 14^{\frac{7}{25}} \cdot 14 \cdot 14^{\frac{7}{25}}\\& = \frac{161}{25} \cdot 14^{\frac{7}{25}} \cdot 14 \cdot 14^{\frac{7}{25}}\\& = \frac{2254}{25} \cdot 14^{\frac{14}{25}}\end{aligned}\]

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