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Answer
The simplified form is \( 2y^{32} \).
Solution
Calculate or simplify the expression \( (256*y^(256))^((1/8)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(256y^{256}\right)^{\frac{1}{8}}\)
- step1: Use the properties of exponents:
\(256^{\frac{1}{8}}\left(y^{256}\right)^{\frac{1}{8}}\)
- step2: Evaluate the power:
\(2y^{32}\)
The simplified form of \( \left(256 y^{256}\right)^{\frac{1}{8}} \) is \( 2y^{32} \).
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Simplify this solution The Deep Dive
To simplify \( \left(256 y^{256}\right)^{\frac{1}{8}} \), we can break it down into two parts. First, \( 256^{\frac{1}{8}} \): since \( 256 = 2^8 \), we have \( 256^{\frac{1}{8}} = (2^8)^{\frac{1}{8}} = 2^{8 \cdot \frac{1}{8}} = 2^1 = 2 \). Next, for \( (y^{256})^{\frac{1}{8}} \), we use the exponent rule \( (a^m)^n = a^{m \cdot n} \) to get \( y^{256 \cdot \frac{1}{8}} = y^{32} \). Putting it all together, we find that \( \left(256 y^{256}\right)^{\frac{1}{8}} = 2y^{32} \). Now you have a neat form: \( 2y^{32} \). That's right, you'd be walking around with a 2-for-1 special: one number and a powerful variable! Math can be fabulous.
