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Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{7}{4}}}{b^{\frac{3}{4}}}$ $\newline$ 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

\frac{b^{\frac{7}{4}}}{b^{\frac{3}{4}}}

\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

______

Apply Quotient Rule: We are given the expression $b^{\frac{7}{4}} / b^{\frac{3}{4}}$ . To simplify this expression, we use the quotient rule of exponents which states that when dividing like bases, we subtract the exponents: $a^m / a^n = a^{m-n}$ .
Subtract Exponents: Applying the quotient rule to our expression, we get $b^{\frac{7}{4} - \frac{3}{4}}$ .
Simplify Result: Subtract the exponents: $\frac{7}{4} - \frac{3}{4} = \frac{4}{4}$ .
Final Simplification: Simplify $\frac{4}{4}$ to get $1$ . So, $b^{\frac{4}{4}} = b^1$ .
Exponent of $1$ : Since any number raised to the power of $1$ is the number itself, $b^1$ is simply $b$ .

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