Question

rewrite the expression in the form $k \cdot y^n$. write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $3y^{\frac{-4}{3}} \cdot 2\sqrt3{y} = $

Explanation:

Step1: Multiply the coefficients

Multiply the constant coefficients 3 and 2.
$3\times2 = 6$

Step2: Rewrite the radical as an exponent

Recall that $\sqrt[3]{y}=y^{\frac{1}{3}}$. So the expression becomes $6\times y^{-\frac{4}{3}}\times y^{\frac{1}{3}}$.

Step3: Use the exponent rule for multiplication

When multiplying with the same base, add the exponents: $a^m\times a^n=a^{m + n}$. Here, $m=-\frac{4}{3}$ and $n=\frac{1}{3}$.
$y^{-\frac{4}{3}+\frac{1}{3}}=y^{-\frac{3}{3}}=y^{-1}$

Step4: Combine the results

Combine the coefficient and the variable part: $6\times y^{-1}=6y^{-1}$ or $\frac{6}{y}$ (but in the form $k\cdot y^n$, it's $6y^{-1}$)

Answer:

$6y^{-1}$ (or equivalently $6\cdot y^{-1}$)