Question

Which values of a and b make the following equation true? (5x7y2)(-4x4y5)=-20xayb

Answer 1

Answer:

a on edge

Step-by-step explanation:

Answer 2

Answer:

The values of a and b are a = 11 , b = 7

Step-by-step explanation:

* Lets explain how to solve the problem

* In the exponential functions we have some rules

1-  In multiplication if they have same base we add  the power

# Ex: b^m  ×  b^n  =  b^(m + n) ⇒ b is the base , m and n are the powers

2- In division if they have same base we subtract  the power

# Ex: b^m  ÷  b^n =  b^(m – n) ⇒ b is the base , m and n are the powers

3- If we have power over power we multiply them

# Ex: (b^m)^n = b^(mn) ⇒ b is the base , m and n are the powers

* Lets solve the problem

∵ The equation is $(5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{a}y^{2}$ ⇒ (1)

- At first multiply the coefficients

∵ -4 × 5 = -20

- Multiply the base x

∵ $(x^{7})(x^{4})=x^{7+4}=x^{11}$

- Multiply the base y

∵ $(y^{2})(y^{5})=y^{2+5}=y^{7}$

∴ $(5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{11}y^{7}$ ⇒ (2)

- By comparing (1) and (2)

∴ a = 11 and b = 7

* The values of a and b are a = 11 , b = 7