By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.
How to simplify an algebraic expression
In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:
[(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] Given
[(3 · a · b²) / (5 · b²)] ÷ [√(9 · a²) / √(100 · b²)] Square root of a division
[(3 · a · b²) / (5 · b²)] ÷ [(√9 · √a²) / (√100 · √b²)] Square root of a product
[(3 · a · b²) / (5 · b²)] ÷ [(3 · a) / (10 · b)] Definition of square root
[(3 · a · b²) · (10 · b)] / [(5 · b²) · (3 · a)] Division of fractions
(30 · a · b³) / (15 · a · b²) Associative and commutative properties / Definition of multiplication / Multiplication of powers of equal base
2 · b Associative and commutative properties / Definition of division / Result
The expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.
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