Radicals
Rational exponents: Products and quotients with negative exponents
Simplify the expression.
$\frac{b^{\frac{3}{2}} b^{- \frac{1}{4}}}{b^{\frac{1}{3}}}$

Write your answer using only positive exponents. Assume that all variables are positive real numbers.

Answer

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Answer

Write the final answer with only positive exponents: $b^{\frac{11}{12}}$

Steps

Step 1 ：Combine the exponents by adding them when multiplying: $b^{\frac{3}{2}} \cdot b^{- \frac{1}{4}} = b^{\frac{3}{2} - \frac{1}{4}}$

Step 2 ：Simplify the exponent: $b^{\frac{3}{2} - \frac{1}{4}} = b^{\frac{6}{4} - \frac{1}{4}} = b^{\frac{5}{4}}$

Step 3 ：Subtract the exponent in the denominator from the exponent in the numerator: $\frac{b^{\frac{5}{4}}}{b^{\frac{1}{3}}} = b^{\frac{5}{4} - \frac{1}{3}}$

Step 4 ：Find a common denominator for the exponents: $b^{\frac{5}{4} - \frac{1}{3}} = b^{\frac{15}{12} - \frac{4}{12}}$

Step 5 ：Simplify the exponent: $b^{\frac{15}{12} - \frac{4}{12}} = b^{\frac{11}{12}}$

Step 6 ：Write the final answer with only positive exponents: $b^{\frac{11}{12}}$

RadicalsRational exponents: Products and quotients with negative exponentsSimplify the expression.b32b−14b13 Write your answer using only positive exponents. Assume that all variables are positive real numbers.

Answer

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Radicals
Rational exponents: Products and quotients with negative exponents
Simplify the expression.
$\frac{b^{\frac{3}{2}} b^{- \frac{1}{4}}}{b^{\frac{1}{3}}}$

Write your answer using only positive exponents. Assume that all variables are positive real numbers.