Simplify. Assume all variables are positive. b^(7/4)/(b^(11/4) * b^(7/4)) Write your answer in the form A or 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. ______

Combine exponents in denominator: We have the expression: b^(7/4) / (b^(11/4) * b^(7/4)) First, let's combine the exponents in the denominator using the property of exponents that states a^m * a^n = a^(m+n).Add exponents in denominator: Combine the exponents in the denominator: b^(11/4) * b^(7/4) = b^(11/4 + 7/4)Simplify exponent in denominator: Add the exponents in the denominator: b^(11/4 + 7/4) = b^(18/4)Divide with subtracted exponents: Simplify the exponent in the denominator: b^(18/4) = b^(4.5) = b^(9/2)Subtract exponents with common denominator: Now we have the expression: b^(7/4) / b^(9/2) To divide two expressions with the same base, we subtract the exponents: a^m / a^n = a^(m-n).Convert to common denominator: Subtract the exponents: b^(7/4) / b^(9/2) = b^(7/4 - 9/2)Apply property for positive exponent: To subtract the exponents, we need a common denominator. The common denominator for 4 and 2 is 4. Convert 9/2 to an expression with a denominator of 4: 9/2 = (9*2)/(2*2) = 18/4Final simplified expression: Now subtract the exponents with a common denominator: b^(7/4 - 18/4) = b^(-11/4)Since we assume all variables are positive and we want the exponent to be positive, we can use the property a^(-n) = 1/a^n to rewrite the expression.Apply the property to get a positive exponent: b^(-11/4) = 1/b^(11/4)The final simplified expression is: 1/b^(11/4)

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Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{7}{4}}}{b^{\frac{11}{4}} \cdot b^{\frac{7}{4}}}$ $\newline$ 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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Q. Simplify. Assume all variables are positive.

\newline

\frac{b^{\frac{7}{4}}}{b^{\frac{11}{4}} \cdot b^{\frac{7}{4}}}

\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

______

Combine exponents in denominator: We have the expression: $b^{\frac{7}{4}} / (b^{\frac{11}{4}} * b^{\frac{7}{4}})$ $\newline$ First, let's combine the exponents in the denominator using the property of exponents that states $a^m * a^n = a^{m+n}$ .
Add exponents in denominator: Combine the exponents in the denominator: $\newline$ $b^{\frac{11}{4}} \cdot b^{\frac{7}{4}} = b^{\frac{11}{4} + \frac{7}{4}}$
Simplify exponent in denominator: Add the exponents in the denominator: $\newline$ $b^{\frac{11}{4} + \frac{7}{4}} = b^{\frac{18}{4}}$
Divide with subtracted exponents: Simplify the exponent in the denominator: $b^{\frac{18}{4}} = b^{4.5} = b^{\frac{9}{2}}$
Subtract exponents with common denominator: Now we have the expression: $b^{\frac{7}{4}} / b^{\frac{9}{2}}$ $\newline$ To divide two expressions with the same base, we subtract the exponents: $a^m / a^n = a^{m-n}$ .
Convert to common denominator: Subtract the exponents: $\newline$ $b^{\frac{7}{4}} / b^{\frac{9}{2}} = b^{\frac{7}{4} - \frac{9}{2}}$
Apply property for positive exponent: To subtract the exponents, we need a common denominator. The common denominator for $4$ and $2$ is $4$ . Convert $\frac{9}{2}$ to an expression with a denominator of $4$ : $\frac{9}{2} = \frac{(9\times2)}{(2\times2)} = \frac{18}{4}$
Final simplified expression: Now subtract the exponents with a common denominator: $b^{\frac{7}{4} - \frac{18}{4}} = b^{-\frac{11}{4}}$
Final simplified expression: Now subtract the exponents with a common denominator: $\newline$ $b^{\frac{7}{4} - \frac{18}{4}} = b^{-\frac{11}{4}}$ Since we assume all variables are positive and we want the exponent to be positive, we can use the property $a^{-n} = \frac{1}{a^n}$ to rewrite the expression.
Final simplified expression: Now subtract the exponents with a common denominator: $\newline$ $b^{\frac{7}{4} - \frac{18}{4}} = b^{-\frac{11}{4}}$ Since we assume all variables are positive and we want the exponent to be positive, we can use the property $a^{-n} = \frac{1}{a^n}$ to rewrite the expression.Apply the property to get a positive exponent: $\newline$ $b^{-\frac{11}{4}} = \frac{1}{b^{\frac{11}{4}}}$
Final simplified expression: Now subtract the exponents with a common denominator: $\newline$ $b^{\frac{7}{4} - \frac{18}{4}} = b^{-\frac{11}{4}}$ Since we assume all variables are positive and we want the exponent to be positive, we can use the property $a^{-n} = \frac{1}{a^n}$ to rewrite the expression.Apply the property to get a positive exponent: $\newline$ $b^{-\frac{11}{4}} = \frac{1}{b^{\frac{11}{4}}}$ The final simplified expression is: $\newline$ $\frac{1}{b^{\frac{11}{4}}}$