Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Rewrite the expression in the form k*z^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). (10root(3)(z))/(2z^(2))=◻$

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). $\newline$ $\frac{10 \sqrt[3]{z}}{2 z^{2}}=\square$

View step-by-step help

Home

Math Problems

Algebra 1

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

\frac{10 \sqrt[3]{z}}{2 z^{2}}=\square

Given expression: We are given the expression $(10\sqrt[3]{z})/(2z^{2})$ . We need to rewrite this expression in the form $k*z^{n}$ . $\newline$ First, let's express the cube root of $z$ as $z$ raised to the power of $1/3$ . $\newline$ Expression: $(10*z^{1/3})/(2z^{2})$
Expressing cube root of $z$ : Now, we simplify the coefficients (numerical parts) of the expression by dividing $10$ by $2$ . $\newline$ $10 / 2 = 5$ $\newline$ So the expression becomes $5 \cdot z^{1/3} / z^{2}$ .
Simplifying coefficients: Next, we apply the laws of exponents to combine the $z$ terms. When dividing like bases, we subtract the exponents. $\frac{z^{\frac{1}{3}}}{z^{2}} = z^{\frac{1}{3} - 2}$
Combining z terms: We need to express $2$ as a fraction with the same denominator as $\frac{1}{3}$ to subtract the exponents easily. $\newline$ $2$ can be written as $\frac{6}{3}$ . $\newline$ So, $z^{\frac{1}{3} - 2}$ becomes $z^{\frac{1}{3} - \frac{6}{3}}$ .
Expressing $2$ as a fraction: Now, subtract the exponents. $\newline$ $\frac{1}{3} - \frac{6}{3} = -\frac{5}{3}$ $\newline$ So, $z^{\frac{1}{3} - \frac{6}{3}} = z^{-\frac{5}{3}}$ .
Subtracting exponents: The final expression is now in the form $k*z^{n}$ , where $k$ is $5$ and $n$ is $-\frac{5}{3}$ . So, $(10\sqrt[3]{z})/(2z^{2}) = 5*z^{-\frac{5}{3}}$ .