20. \( -5 x(-2 x y z)^{0} \) 21. \( \frac{7 a^{2} b^{-3} \times 3 a^{-3} b^{0}}{14 a^{-1} b} \) 22. \( \frac{16 a b^{-2} \times 125 a^{-1} b^{3}}{80 a^{2} b^{5}} \) 23. \( 5\left(2 p q^{3}\right)\left(3 p q^{-2}\right) \) 24. \( \sqrt{5 a p^{2}} \times \sqrt{20 a^{3}} \) 25. \( \frac{8 x^{2} y^{-1} \times 3 x^{3} y^{-5}}{} \)

Simplify the expression by following steps: - step0: Solution: \(\left(8x^{2}y^{-1}\times 3x^{3}y^{-5}\right)\) - step1: Evaluate: \(8x^{2}y^{-1}\times 3x^{3}y^{-5}\) - step2: Multiply the terms: \(24x^{2}y^{-1}x^{3}y^{-5}\) - step3: Multiply the terms: \(24x^{2+3}y^{-1}\times y^{-5}\) - step4: Add the numbers: \(24x^{5}y^{-1}\times y^{-5}\) - step5: Multiply the terms: \(24x^{5}y^{-1-5}\) - step6: Subtract the numbers: \(24x^{5}y^{-6}\) - step7: Simplify: \(\frac{24x^{5}}{y^{6}}\) Calculate or simplify the expression \( 5 * (2 * p * q^{3}) * (3 * p * q^{-2}) \). Simplify the expression by following steps: - step0: Solution: \(5\left(2pq^{3}\right)\left(3pq^{-2}\right)\) - step1: Evaluate: \(5\times 2pq^{3}\left(3pq^{-2}\right)\) - step2: Remove the parentheses: \(5\times 2pq^{3}\times 3pq^{-2}\) - step3: Multiply the terms: \(30pq^{3}pq^{-2}\) - step4: Multiply the terms: \(30p^{2}q^{3}\times q^{-2}\) - step5: Multiply the terms: \(30p^{2}q^{3-2}\) - step6: Subtract the numbers: \(30p^{2}q\) Calculate or simplify the expression \( -5 * x * (-2 * x * y * z)^{0} \). Simplify the expression by following steps: - step0: Solution: \(-5x\left(-2xyz\right)^{0}\) - step1: Multiply the terms: \(-5x\) Calculate or simplify the expression \( (16 * a * b^{-2} * 125 * a^{-1} * b^{3}) / (80 * a^{2} * b^{5}) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(16ab^{-2}\times 125a^{-1}b^{3}\right)}{\left(80a^{2}b^{5}\right)}\) - step1: Evaluate: \(\frac{\left(16ab^{-2}\times 125a^{-1}b^{3}\right)}{80a^{2}b^{5}}\) - step2: Remove the parentheses: \(\frac{16ab^{-2}\times 125a^{-1}b^{3}}{80a^{2}b^{5}}\) - step3: Multiply: \(\frac{2000b}{80a^{2}b^{5}}\) - step4: Reduce the fraction: \(\frac{25}{a^{2}b^{4}}\) Calculate or simplify the expression \( \sqrt(5 * a * p^{2}) * \sqrt(20 * a^{3}) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{5ap^{2}}\times \sqrt{20a^{3}}\) - step1: Simplify the root: \(p\sqrt{5a}\times \sqrt{20a^{3}}\) - step2: Simplify the root: \(p\sqrt{5a}\times 2a\sqrt{5a}\) - step3: Calculate: \(p\times 2a\times 5a\) - step4: Multiply the terms: \(10pa\times a\) - step5: Multiply the terms: \(10pa^{2}\) Calculate or simplify the expression \( (7 * a^{2} * b^{-3} * 3 * a^{-3} * b^{0}) / (14 * a^{-1} * b) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(7a^{2}b^{-3}\times 3a^{-3}b^{0}\right)}{\left(14a^{-1}b\right)}\) - step1: Remove the parentheses: \(\frac{7a^{2}b^{-3}\times 3a^{-3}b^{0}}{14a^{-1}b}\) - step2: Multiply by \(a^{-n}:\) \(\frac{7a^{2}b^{-3}\times 3a^{-3}b^{0}ab^{-1}}{14}\) - step3: Evaluate the power: \(\frac{7a^{2}b^{-3}\times 3a^{-3}\times 1\times ab^{-1}}{14}\) - step4: Calculate: \(\frac{7a^{2}b^{-3}\times 3a^{-3}\times ab^{-1}}{14}\) - step5: Multiply: \(\frac{21b^{-4}}{14}\) - step6: Reduce the fraction: \(\frac{3b^{-4}}{2}\) - step7: Rewrite the expression: \(\frac{\frac{3}{b^{4}}}{2}\) - step8: Simplify: \(\frac{3}{2b^{4}}\) Here are the simplified results for each expression: 20. For the expression \( -5 x(-2 x y z)^{0} \): - Since any non-zero number raised to the power of 0 is 1, we have: \[ -5 x(-2 x y z)^{0} = -5 x \cdot 1 = -5x \] 21. For the expression \( \frac{7 a^{2} b^{-3} \times 3 a^{-3} b^{0}}{14 a^{-1} b} \): - First, simplify the numerator: \[ 7 a^{2} b^{-3} \times 3 a^{-3} b^{0} = 21 a^{2 - 3} b^{-3 + 0} = 21 a^{-1} b^{-3} \] - Now, simplify the entire expression: \[ \frac{21 a^{-1} b^{-3}}{14 a^{-1} b} = \frac{21}{14} \cdot \frac{a^{-1}}{a^{-1}} \cdot \frac{b^{-3}}{b} = \frac{3}{2b^{4}} \] 22. For the expression \( \frac{16 a b^{-2} \times 125 a^{-1} b^{3}}{80 a^{2} b^{5}} \): - Simplifying the numerator: \[ 16 a b^{-2} \times 125 a^{-1} b^{3} = 2000 a^{1 - 1} b^{-2 + 3} = 2000 b^{1} \] - Now, simplify the entire expression: \[ \frac{2000 b}{80 a^{2} b^{5}} = \frac{2000}{80} \cdot \frac{b^{1}}{b^{5}} = \frac{25}{a^{2}b^{4}} \] 23. For the expression \( 5\left(2 p q^{3}\right)\left(3 p q^{-2}\right) \): - Simplifying: \[ 5 \cdot 2 p q^{3} \cdot 3 p q^{-2} = 30 p^{1 + 1} q^{3 - 2} = 30 p^{2} q \] 24. For the expression \( \sqrt{5 a p^{2}} \times \sqrt{20 a^{3}} \): - Using the property of square roots: \[ \sqrt{5 a p^{2} \times 20 a^{3}} = \sqrt{100 a^{4} p^{2}} = 10 a^{2} p \] 25. For the expression \( \frac{8 x^{2} y^{-1} \times 3 x^{3} y^{-5}}{} \): - Simplifying the numerator: \[ 8 x^{2} y^{-1} \times 3 x^{3} y^{-5} = 24 x^{2 + 3} y^{-1 - 5} = 24 x^{5} y^{-6} \] - Since there is no denominator, the result is: \[ \frac{24 x^{5}}{y^{6}} \] In summary, the simplified results are: - 20: \( -5x \) - 21: \( \frac{3}{2b^{4}} \) - 22: \( \frac{25}{a^{2}b^{4}} \) - 23: \( 30p^{2}q \) - 24: \( 10pa^{2} \) - 25: \( \frac{24x^{5}}{y^{6}} \)