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If 2ⁿ = y, find 2^(2+n/3)

June 7, 2026Mathematics

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Step-by-step solution

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Break down the exponent in the expression $2^{(2+\frac{n}{3})}$ using the exponent rule $a^{m+n} = a^m \cdot a^n$ .
$2^{(2+\frac{n}{3})} = 2^2 \cdot 2^{\frac{n}{3}}$
Simplify $2^2$ and rewrite $2^{\frac{n}{3}}$ using the exponent rule $(a^m)^n = a^{mn}$ .
$2^2 = 4$ $2^{\frac{n}{3}} = (2^n)^{\frac{1}{3}}$
Substitute the given value $2^n = y$ into the expression.
$4 \cdot (2^n)^{\frac{1}{3}} = 4 \cdot y^{\frac{1}{3}}$
Express the fractional exponent as a root.
$y^{\frac{1}{3}} = \sqrt[3]{y}$
So, the expression becomes:
$4\sqrt[3]{y}$
The simplified expression is:
\boxed{\textbf{4\sqrt[3]{y}}}

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