Simplify. Assume all variables are positive. $\newline$ $b^{\frac{1}{7}} \cdot b^{\frac{1}{7}}$ $\newline$ 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

b^{\frac{1}{7}} \cdot b^{\frac{1}{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 Equation: Identify the equation and apply the product of powers property. $\newline$ The product of powers property states that when you multiply two exponents with the same base, you add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ So, $b^{1/7} \times b^{1/7} = b^{1/7 + 1/7}$ .
Apply Product Property: Add the exponents. $\newline$ $\frac{1}{7} + \frac{1}{7} = \frac{2}{7}$ . $\newline$ So, $b^{\frac{1}{7}} \times b^{\frac{1}{7}} = b^{\frac{2}{7}}$ .
Add Exponents: 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 $b^{\frac{2}{7}}$ , which is already in the correct form.