Simplify. Assume all variables are positive. $\newline$ $z^{\frac{5}{7}} \cdot z^{\frac{12}{7}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

z^{\frac{5}{7}} \cdot z^{\frac{12}{7}}

\newline

Write your answer in the form

A

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Identify and Apply Exponent Rule: Identify the equation and apply the exponent rule for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $z^{\frac{5}{7}} \times z^{\frac{12}{7}} = z^{\frac{5}{7} + \frac{12}{7}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{5}{7} + \frac{12}{7} = \left(\frac{5 + 12}{7}\right) = \frac{17}{7}$ . $\newline$ So, $z^{\frac{5}{7}} \cdot z^{\frac{12}{7}} = z^{\frac{17}{7}}$ .
Write Final Answer: Write the final answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ The final answer is $z^{\frac{17}{7}}$ .