Question

simplify. assume all variables are positive.$b^{-\frac{1}{4}} cdot b^{\frac{9}{4}}$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.

Explanation:

Step1: Apply exponent product rule

When multiplying like bases, add exponents: $b^m \cdot b^n = b^{m+n}$
$b^{-\frac{1}{4}} \cdot b^{\frac{2}{4}} = b^{-\frac{1}{4}+\frac{2}{4}}$

Step2: Add the exponents

Calculate the sum of the fractions.
$b^{\frac{-1+2}{4}} = b^{\frac{1}{4}}$

Answer:

$b^{\frac{1}{4}}$