8类RD Sharma解决方案–第六章代数表达式和恒等式–练习6.3 |套装1

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问题1： 5x ² * 4x ³

解决方案：

First, separate the numbers and variables. 

= (5 * 4) * (x² * x³) 

Add the powers of the same variable and multiply the numbers.

= 20 * (x²⁺³)

= 20x⁵

问题2： -3a ² * 4b ⁴

解决方案：

First, separate the numbers and variables.

= (-3 * 4) * (a²) * (b⁴)

= -12a²b⁴

问题3： (-5xy)*(-3x ² yz)

解决方案：

First separate the numbers and variables.  

= (-5 * -3) * (x * x²) * (y * y) * (z)

Add the powers of the same variable and multiply the numbers.

= 15 * (x¹⁺²) * (y¹⁺¹) * (z)

= 15x³y²z

问题4： (1/2)xy *(2/3)x ² yz ²

解决方案：

First separate the numbers and variables.  

= ((1/2) * (2/3)) * (x * x²) * (y * y) * (z²)

Add the powers of the same variable and multiply the numbers.

= (1/3) * (x¹⁺²) * (y¹⁺¹) * (z²)

= (1/3)x³y²z²

问题5： ((-7/5)xy ² z)*((13/3)x ² yz ² )

解决方案：

First separate the numbers and variables.  

= ((-7/5) * (13/3)) * (x * x²) * (y² * y) * (z * z²)

Add the powers of the same variable and multiply the numbers.

= (-91/15) * (x¹⁺²) * (y^{2 +1})  ^*  (z¹⁺²)

= (-91/15)x³y³z³

问题6：   ((-24/25)x ³ z)*((-15/16)xz ² y)

解决方案：

First separate the numbers and variables. 

= ((-24/25) * (-15/16)) * (x³ * x) * (z * z²) * (y) 

Add the powers of the same variable and multiply the numbers.

= (9/4) * (x³⁺¹) * (z¹⁺²) * (y)

= (9/10)x⁴yz³

问题7： ((-1/27)a ² b ² )*((9/2))a ³ b ² c ² )

解决方案：

First separate the numbers and variables. 

= ((-1/27)) * (9/2)) * (a² * a³) * (b²  *  b²) * (c²)

Add the powers of the same variable and multiply the numbers.

= (-1/6) * (a²⁺³) * (b²⁺²) * (c²)

= (-1/6)a⁵b⁴c²

问题8： (-7xy)*((1/4)x ² yz)

解决方案：

First separate the numbers and variables. 

= (-7 * (1/4)) * (x * x²) * (y * y) * (z)

Add the powers of the same variable and multiply the numbers.

= (-7 * (1/4)) * (x¹⁺²) * (y¹⁺¹) * (z)

= (-7/4) x³y²z

问题9： (7ab)*(-5ab ² c)*(6abc ² )

解决方案：

First separate the numbers and variables. 

= (7 * -5 * 6) * (a * a * a) * (b * b² * b) * (c * c²)

Add the powers of the same variable and multiply the numbers.

= -210 * (a¹⁺¹⁺¹) * (b¹⁺²⁺¹) * (c¹⁺²)

= -210a³b⁴c³

问题10： (-5a)*(-10a ² )*(- ^{2a 3} )

解决方案：

First separate the numbers and variables. 

= (-5 * -10 * -2) * (a * a²  * a³)

Add the powers of the same variable and multiply the numbers.

= (-100) * (a¹⁺²⁺³)

= -100a⁶ 

问题11： (-4x ² )*(-6xy ² )*( ^{3yz 2} )

解决方案：

First separate the numbers and variables.

= (-4 * -6 * 3) * (x² * x) * (y² * y) * (z²)

Add the powers of the same variable and multiply the numbers.

= -72 * (x²⁺¹) * (y²⁺¹) * (z²)

= -72x³y³z²

问题12： ((-2/7)a ⁴ )*((-3/4)a ² b)*((-14/5)b ² )

解决方案：

First separate the numbers and variables.

= ((-2/7) * (-3/4) * (-14/5)) * (a⁴  * a²) * (b * b²)

Add the powers of the same variable and multiply the numbers.

= (-3/5) * (a⁴⁺²) * (b¹⁺²)

= (-3/5)a⁶b³

问题13： ((7/9)ab ² )*((15/7)ac ² b)*((-3/5)a ² c)

解决方案：

First separate the numbers and variables.

= ((7/9) * (15/7) * (-3/5)) * (a * a * a²) * (b² * b) * (c² * c)

Add the powers of the same variable and multiply the numbers.

= (-1) * (a¹⁺¹⁺²) * (b²⁺¹) * (c²⁺¹)

= -a⁴b³c³

问题14： ((4/3)u ² vw)*(-5uvw ² )*((1/3)v ² wu)

解决方案：

First separate the numbers and variables.

= ((4/3) * (-5) * (1/3)) * (u²  * u * u) * (v * v * v²) * (w * w² * w)

Add the powers of the same variable and multiply the numbers.

= (-20/9) * (u²⁺¹⁺¹) * (v¹⁺¹⁺²) * (w¹⁺²⁺¹)

= (-20/9)u⁴v⁴w⁴

问题15： (0.5x)*((1/3)xy ² z ⁴ )*(24x ² yz)

解决方案：

First separate the numbers and variables.

= ((0.5) * (1/3) * (24)) * (x * x * x²) * (y² * y) * (z⁴ * z)

Add the powers of the same variable and multiply the numbers.

= (4) * (x¹⁺¹⁺²) * (y²⁺¹) * (z⁴⁺¹)

= 4x⁴y³z⁵

问题16 (((4/3)pq ² )*((-1/4)p ² r)*(16p ² q ² r ² )

解决方案：

First separate the numbers and variables.

= (( 4/3) * (-1/4) * (16)) * (p * p² * p²) * (q²  * q²) * (r * r²)

Add the powers of the same variable and multiply the numbers.

= (-16/3) * (p¹⁺²⁺²) * (q²⁺²) * (r¹⁺²)

= (-16/3)p⁵q⁴r³

问题17： (2.3xy)*(0.1x)*(0.16)

解决方案：

First separate the numbers and variables.

= (2.3 * 0.1 * 0.16) *  (x * x) * (y)

Add the powers of the same variable and multiply the numbers.

= 0.0368 * (x¹⁺¹) * (y)

= 0.0368x²y 

第6章代数表达式和恒等式–练习6.3 |套装2