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

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

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Math Problems

Algebra 2

Evaluate variable expressions involving rational numbers

Full solution

Q. Rewrite the expression in the form

k \cdot z^{n}

\newline

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

\newline

3 \sqrt[4]{z} \cdot 3 z^{\frac{3}{4}}=

Rewrite expression: We need to express the given expression in the form of $kz^{n}$ . The given expression is $3\sqrt[4]{z}\cdot3z^{\frac{3}{4}}$ . The $4$ th root of $z$ can be written as $z^{\frac{1}{4}}$ , so we rewrite the expression as $3z^{\frac{1}{4}}\cdot3z^{\frac{3}{4}}$ .
Multiply coefficients and exponents: Now we multiply the coefficients ( $3$ and $3$ ) and add the exponents of $z$ (( $1/4$ ) and ( $3/4$ )) because when we multiply terms with the same base, we add their exponents. $\newline$ $3 \times 3 = 9$ $\newline$ $(1/4) + (3/4) = 1$ $\newline$ So, the expression becomes $9z^{1}$ .
Final form: The expression $9z^{1}$ is already in the form of $k*z^{n}$ , where $k$ is $9$ and $n$ is $1$ .