Question

simplify. assume all variables are positive.
$b^{\frac{-5}{7}} \cdot b^{\frac{9}{7}}$
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 terms with the same base, add exponents: $b^m \cdot b^n = b^{m+n}$.
$$b^{-\frac{5}{7}} \cdot b^{\frac{9}{7}} = b^{-\frac{5}{7} + \frac{9}{7}}$$

Step2: Add the exponents

Calculate the sum of the fractional exponents.
$$b^{\frac{-5 + 9}{7}} = b^{\frac{4}{7}}$$

Answer:

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