Question

1)(5b)² +15/5b² +3= 2)(5a²)³ × (6b)² / (30a³b)²=

Answer 1

1)
$(5b) {}^{2} + \frac{15 {}^{2} }{5b} + 3 = \frac{25b + {}^{3 } +3b + 45 }{b}$
2)
$(5a {}^{2} ) {}^{3} \times \frac{(6b) {}^{2} }{(30a {}^{3}b) {}^{2} } = 125 \times \frac{1}{25} = 5 \times 1 = 5$

Answer 2

Let's simplify the given expressions step by step:

1. (5b)² + 15 / 5b² + 3

Step 1: Square the first term. (5b)² = 25b²

Step 2: Simplify the middle term. 15 / 5b² = 3 / b²

Step 3: Combine the terms and the constant. 25b² + 3 / b² + 3

This expression cannot be further simplified because we have terms with different powers of 'b' in the numerator and denominator.

2. (5a²)³ × (6b)² / (30a³b)²

Step 1: Cube the first term. (5a²)³ = 125a^6

Step 2: Square the second term. (6b)² = 36b²

Step 3: Square the denominator term. (30a³b)² = (30)²(a³)²(b²)² = 900a^6b^4

Step 4: Combine the terms. 125a^6 × 36b² / 900a^6b^4

Step 5: Simplify further. 125/900 = 5/36

Final result: 5a^6b² / 36b^4

We could also simplify the expression by canceling out common factors in the numerator and denominator, but no further simplification is possible since the powers of 'a' and 'b' in the numerator and denominator are different.