Simplify the following algebraic expressions: 1) (9p8q5r2)/(3p8q5r2) 2) 2(m3)0 - (2m3)0 3) (-4)2 x (2)2 + (-3)0.

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Asked on April 27, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-27T17:45:14.654Z

Welcome back Lerato — missed you this week. Here are the solutions to the problems. 1) Simplify (9p^8q^5r^2)/(3p^8q^5r^2). Step 1: Separate the coefficients and variables. (9p^8q^5r^2)/(3p^8q^5r^2) = (9)/(3) × (p^8)/(p^8) × (q^5)/(q^5) × (r^2)/(r^2) Step 2: Simplify each part. (9)/(3) = 3 (p^8)/(p^8) = p^8-8 = p^0 = 1 (q^5)/(q^5) = q^5-5 = q^0 = 1 (r^2)/(r^2) = r^2-2 = r^0 = 1 Step 3: Multiply the simplified parts. 3 × 1 × 1 × 1 = 3 The simplified expression is 3. 2) Simplify 2(m^3)^0 - (2m^3)^0. Step 1: Apply the exponent rule (a^b)^0 = 1 and a^0 = 1. For the first term, (m^3)^0 = 1. So, 2(m^3)^0 = 2 × 1 = 2. For the second term, (2m^3)^0 = 1 because the entire term inside the parentheses is raised to the power of 0. Step 2: Substitute the simplified terms back into the expression. 2 - 1 Step 3: Perform the subtraction. 2 - 1 = 1 The simplified expression is 1. 3) Simplify (-4)^2 × (2)^2 + (-3)^0. Step 1: Evaluate each term. (-4)^2 = (-4) × (-4) = 16 (2)^2 = 2 × 2 = 4 (-3)^0 = 1 (Any non-zero number raised to the power of 0 is 1) Step 2: Substitute the values back into the expression. 16 × 4 + 1 Step 3: Perform the multiplication. 16 × 4 = 64 Step 4: Perform the addition. 64 + 1 = 65 The simplified expression is 65. 4) Simplify (31260xy)^0 × (5x^2). Step 1: Apply the exponent rule a^0 = 1. For the first term, (31260xy)^0 = 1 because the entire term inside the parentheses is raised to the power of 0. Step 2: Substitute the simplified term back into the expression. 1 × (5x^2) Step 3: Perform the multiplication. 1 × 5x^2 = 5x^2 The simplified expression is 5x^2. 5) Simplify (50x^8y^3z^2)/(25x^8y^3z^2). Step 1: Separate the coefficients and variables. (50x^8y^3z^2)/(25x^8y^3z^2) = (50)/(25) × (x^8)/(x^8) × (y^3)/(y^3) × (z^2)/(z^2) Step 2: Simplify each part. (50)/(25) = 2 (x^8)/(x^8) = x^8-8 = x^0 = 1 (y^3)/(y^3) = y^3-3 = y^0 = 1 (z^2)/(z^2) = z^2-2 = z^0 = 1 Step 3: Multiply the simplified parts. 2 × 1 × 1 × 1 = 2 The simplified expression is 2. Send me the next one 📸

Accepted Answer · 2026-04-27T17:45:14.654Z

Welcome back Lerato — missed you this week. Here are the solutions to the problems. 1) Simplify (9p^8q^5r^2)/(3p^8q^5r^2). Step 1: Separate the coefficients and variables. (9p^8q^5r^2)/(3p^8q^5r^2) = (9)/(3) × (p^8)/(p^8) × (q^5)/(q^5) × (r^2)/(r^2) Step 2: Simplify each part. (9)/(3) = 3 (p^8)/(p^8) = p^8-8 = p^0 = 1 (q^5)/(q^5) = q^5-5 = q^0 = 1 (r^2)/(r^2) = r^2-2 = r^0 = 1 Step 3: Multiply the simplified parts. 3 × 1 × 1 × 1 = 3 The simplified expression is 3. 2) Simplify 2(m^3)^0 - (2m^3)^0. Step 1: Apply the exponent rule (a^b)^0 = 1 and a^0 = 1. For the first term, (m^3)^0 = 1. So, 2(m^3)^0 = 2 × 1 = 2. For the second term, (2m^3)^0 = 1 because the entire term inside the parentheses is raised to the power of 0. Step 2: Substitute the simplified terms back into the expression. 2 - 1 Step 3: Perform the subtraction. 2 - 1 = 1 The simplified expression is 1. 3) Simplify (-4)^2 × (2)^2 + (-3)^0. Step 1: Evaluate each term. (-4)^2 = (-4) × (-4) = 16 (2)^2 = 2 × 2 = 4 (-3)^0 = 1 (Any non-zero number raised to the power of 0 is 1) Step 2: Substitute the values back into the expression. 16 × 4 + 1 Step 3: Perform the multiplication. 16 × 4 = 64 Step 4: Perform the addition. 64 + 1 = 65 The simplified expression is 65. 4) Simplify (31260xy)^0 × (5x^2). Step 1: Apply the exponent rule a^0 = 1. For the first term, (31260xy)^0 = 1 because the entire term inside the parentheses is raised to the power of 0. Step 2: Substitute the simplified term back into the expression. 1 × (5x^2) Step 3: Perform the multiplication. 1 × 5x^2 = 5x^2 The simplified expression is 5x^2. 5) Simplify (50x^8y^3z^2)/(25x^8y^3z^2). Step 1: Separate the coefficients and variables. (50x^8y^3z^2)/(25x^8y^3z^2) = (50)/(25) × (x^8)/(x^8) × (y^3)/(y^3) × (z^2)/(z^2) Step 2: Simplify each part. (50)/(25) = 2 (x^8)/(x^8) = x^8-8 = x^0 = 1 (y^3)/(y^3) = y^3-3 = y^0 = 1 (z^2)/(z^2) = z^2-2 = z^0 = 1 Step 3: Multiply the simplified parts. 2 × 1 × 1 × 1 = 2 The simplified expression is 2. Send me the next one 📸

Simplify the following algebraic expressions: 1) (9p8q5r2)/(3p8q5r2) 2) 2(m3)0 - (2m3)0 3) (-4)2 x (2)2 + (-3)0.

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Simplify the following algebraic expressions: 1) (9p8q5r2)/(3p8q5r2) 2) 2(m3)0 - (2m3)0 3) (-4)2 x (2)2 + (-3)0.

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