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$Rewrite the expression in the form k*y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). 3y^(-(4)/(3))*2root(3)(y)=$

Rewrite the expression in the form $k \cdot y^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $3 y^{-\frac{4}{3}} \cdot 2 \sqrt[3]{y}=$

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Math Problems

Algebra 1

Evaluate variable expressions involving rational numbers

Full solution

Q. Rewrite the expression in the form

k \cdot y^{n}

\newline

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

\newline

3 y^{-\frac{4}{3}} \cdot 2 \sqrt[3]{y}=

Identify expression and components: Identify the given expression and the components that need to be rewritten. $\newline$ Expression: $3y^{-(\frac{4}{3})}\cdot 2\sqrt[3]{y}$ $\newline$ We need to rewrite the cube root of $y$ as $y$ raised to a power.
Rewrite cube root of y: Rewrite the cube root of $y$ as $y$ raised to the power of $\frac{1}{3}$ . $2\sqrt[3]{y}$ is equivalent to $2y^{\frac{1}{3}}$ .
Combine terms: Combine the two terms by multiplying the coefficients and adding the exponents of $y$ . The coefficients $3$ and $2$ multiply to give $6$ . The exponents $-\frac{4}{3}$ and $\frac{1}{3}$ add to give $-\frac{4}{3} + \frac{1}{3} = -\frac{3}{3} = -1$ . Expression becomes: $6y^{-1}$ .
Check required form: Check if the expression is in the required form $k*y^{n}$ . $\newline$ The expression $6y^{-1}$ is in the form $k*y^{n}$ , where $k=6$ and $n=-1$ .