If 2^n = y, find 2^(2+n/3)

June 7, 2026Mathematics

ScanSolve AI Answer

June 7, 2026

Answer

$\textbf{4\sqrt[3]{y}}$

Step 1: Break down the exponent in the expression $2^{(2+\frac{n}{3})}$ using the exponent rule $a^{m+n} = a^m \cdot a^n$ . $2^{(2+\frac{n}{3})} = 2^2 \cdot 2^{\frac{n}{3}}$

Step 2: Simplify $2^2$ and rewrite $2^{\frac{n}{3}}$ using the exponent rule $(a^m)^n = a^{mn}$ . $2^2 = 4$ $2^{\frac{n}{3}} = (2^n)^{\frac{1}{3}}$

Step 3: Substitute the given value $2^n = y$ into the expression. $4 \cdot (2^n)^{\frac{1}{3}} = 4 \cdot y^{\frac{1}{3}}$

Step 4: 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: $\boxed{4\sqrt[3]{y}}$ Drop the next question!

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Quick Answer

Break down the exponent in the expression 2^(2+(n)/(3)) using the exponent rule a^m+n = a^m · a^n.

Asked on June 7, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 7, 2026

Step 1: Break down the exponent in the expression 2^(2+(n)/(3)) using the exponent rule a^m+n = a^m · a^n. 2^(2+(n)/(3)) = 2^2 · 2^(n)/(3) Step 2: Simplify 2^2 and rewrite 2^(n)/(3) using the exponent rule (a^m)^n = a^mn. 2^2 = 4 2^(n)/(3) = (2^n)^(1)/(3) Step 3: Substitute the given value 2^n = y into the expression. 4 · (2^n)^(1)/(3) = 4 · y^(1)/(3) Step 4: Express the fractional exponent as a root. y^(1)/(3) = [3]y So, the expression becomes: 4[3]y The simplified expression is: 4[3]y Drop the next question!

Asked on June 7, 2026Mathematics

ScanSolve AI AnswerAnswered on June 7, 2026

Step 1: Break down the exponent in the expression 2^(2+(n)/(3)) using the exponent rule a^m+n = a^m · a^n. 2^(2+(n)/(3)) = 2^2 · 2^(n)/(3) Step 2: Simplify 2^2 and rewrite 2^(n)/(3) using the exponent rule (a^m)^n = a^mn. 2^2 = 4 2^(n)/(3) = (2^n)^(1)/(3) Step 3: Substitute the given value 2^n = y into the expression. 4 · (2^n)^(1)/(3) = 4 · y^(1)/(3) Step 4: Express the fractional exponent as a root. y^(1)/(3) = [3]y So, the expression becomes: 4[3]y The simplified expression is: 4[3]y Drop the next question!