Question

(-1\2b3)(8b2) 2) (7a5b3c)(-3ab4c) 3 ) (-3\2a3xy3)3\4ax2y) 4) (-18n)(-1\6m2)(-5nm) 5) (-13a2bc)(-5ab2c)(-0.4abc3)

Answer 1

1) (-1/2b×2)(8b×2) = -b×16b= -16b²

2) (7a×5b×3c)(-3ab×4c) = 75abc × (- 12abc) = -900a²b²c²

3) ( -3/2a × 3xy×3) × 3/4ax×2y = - 27/2axy × 3/2axy = -81/4 axy = 20,25axy

4) ( -18n)( -1/6m×2)( -5mn) = -18n × ( - 1/3m)( -5nm) = 6mn × ( -5mn) = -30m²n²

5) ( -5ab × 2c)( -0,4abc×3) = -10abc × ( - 1.2abc) = 12a²b²c²

Answer 2

To simplify the given expressions, follow these steps for each one:

1. $(-1/2b^3)(8b^2)$

Step 1: Multiply the constants: $(-1/2) \times 8 = -4$ Step 2: Multiply the variables with the same base, and add their exponents: $b^3 \times b^2 = b^{3+2} = b^5$

The simplified expression is $-4b^5$.

2. $(7a^5b^3c)(-3ab^4c)$

Step 1: Multiply the constants: $7 \times -3 = -21$ Step 2: Multiply the variables with the same base, and add their exponents: $a^5 \times a = a^{5+1} = a^6$ $b^3 \times b^4 = b^{3+4} = b^7$ $c \times c = c^2$

The simplified expression is $-21a^6b^7c^2$.

3. $(-3/2a^3xy^3) \div (4ax^2y)$

When dividing, we can multiply by the reciprocal of the divisor:

$(-3/2a^3xy^3) \times \frac{1}{4ax^2y}$

Step 1: Multiply the constants: $(-3/2) \times \frac{1}{4} = -\frac{3}{8}$ Step 2: Divide the variables with the same base, and subtract their exponents: $a^3 \div a = a^{3-1} = a^2$ $x \div x^2 = x^{1-2} = x^{-1} = \frac{1}{x}$ $y^3 \div y = y^{3-1} = y^2$

The simplified expression is $-\frac{3}{8}a^2 \frac{1}{x}y^2$, or $-\frac{3}{8a^2xy^2}$.

4. $(-18n) \times \left(-\frac{1}{6}m^2\right) \times (-5nm)$

Step 1: Multiply the constants: $(-18) \times \left(-\frac{1}{6}\right) \times (-5) = 30$ Step 2: Multiply the variables with the same base, and add their exponents: $n \times m = nm$ (Note that $n \times -n = -n^2$, but here they are different variables, so we leave them as separate terms)

The simplified expression is $30nm$.

5. $(-13a^2bc) \times (-5ab^2c) \times (-0.4abc^3)$

Step 1: Multiply the constants: $(-13) \times (-5) \times (-0.4) = 26$ Step 2: Multiply the variables with the same base, and add their exponents: $a^2 \times a = a^{2+1} = a^3$ $b \times b^2 = b^{1+2} = b^3$ $c \times c \times c^3 = c^{1+1+3} = c^5$