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Simplify. Assume all variables are positive. $\newline$ $b^{\frac{1}{6}} \cdot b^{\frac{5}{6}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

b^{\frac{1}{6}} \cdot b^{\frac{5}{6}}

\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

______

Identify and apply property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying powers with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $b^{\frac{1}{6}} \times b^{\frac{5}{6}} = b^{\frac{1}{6} + \frac{5}{6}}$ .
Add exponents: Add the exponents. $\newline$ $\frac{1}{6} + \frac{5}{6} = \frac{6}{6}$ . $\newline$ $b^{\frac{1}{6} + \frac{5}{6}} = b^{\frac{6}{6}}$ .
Simplify exponent: Simplify the exponent. $\newline$ $\frac{6}{6}$ is equal to $1$ . $\newline$ $b^{\frac{6}{6}} = b^1$ .
Simplify expression: Simplify the expression. $\newline$ $b^1$ is simply $b$ . $\newline$ So, $b^{\frac{1}{6}} \times b^{\frac{5}{6}} = b$ .

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