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Rewrite the expression in the form k*y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). (4root(4)(y^(5)))^((1)/(2))=2

Rewrite the expression in the form k⋅yn k \cdot y^{n} . Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newline(4y54)12=2 \left(4 \sqrt[4]{y^{5}}\right)^{\frac{1}{2}}=2

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Full solution

Q. Rewrite the expression in the form k⋅yn k \cdot y^{n} . Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newline(4y54)12=2 \left(4 \sqrt[4]{y^{5}}\right)^{\frac{1}{2}}=2
  1. Rewrite expression inside parentheses: First, let's rewrite the expression inside the parentheses. The fourth root of y5 y^5 is y5/4 y^{5/4} . y54=y5/4 \sqrt[4]{y^5} = y^{5/4}
  2. Raise expression to power: Now, we need to raise y54y^{\frac{5}{4}} to the power of 12\frac{1}{2}. (y54)12=y(54⋅12)=y58(y^{\frac{5}{4}})^{\frac{1}{2}} = y^{(\frac{5}{4} \cdot \frac{1}{2})} = y^{\frac{5}{8}}
  3. Simplify expression: So, the expression (4y54)12 \left( 4 \sqrt[4]{y^{5}} \right)^{\frac{1}{2}} simplifies to y58 y^{\frac{5}{8}} .
  4. Rewrite in k∗ynk*y^n form: But we need to rewrite it in the form k∗ynk*y^{n}. Here, k=1k=1 and n=58n=\frac{5}{8}.

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