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The simplified form is \( 4y^{6} \).
Solución
Calculate or simplify the expression \( (32*y^(15))^((2/5)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(32y^{15}\right)^{\frac{2}{5}}\)
- step1: Use the properties of exponents:
\(32^{\frac{2}{5}}\left(y^{15}\right)^{\frac{2}{5}}\)
- step2: Evaluate the power:
\(4y^{6}\)
The simplified form of \( \left(32 y^{15}\right)^{\frac{2}{5}} \) is \( 4y^{6} \).
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Simplifique esta solución Bonus Knowledge
To simplify \( \left(32 y^{15}\right)^{\frac{2}{5}} \), we can separate the expression inside the parentheses into its components. Starting with the numeric part, \( 32^{\frac{2}{5}} \) can be calculated. Since \( 32 = 2^5 \), we have: \[ 32^{\frac{2}{5}} = \left(2^5\right)^{\frac{2}{5}} = 2^{5 \cdot \frac{2}{5}} = 2^{2} = 4. \] Now for the variable part, \( (y^{15})^{\frac{2}{5}} = y^{15 \cdot \frac{2}{5}} = y^{6}. \) Putting it all together, we get: \[ \left(32 y^{15}\right)^{\frac{2}{5}} = 4 y^{6}. \] Thus, the simplified expression is \( 4y^6 \).
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