Grade 7 math exponents

Introduction to exponents:

In this article we discuss grade 7 math exponents solving problems. The exponents is the function ex, where e is the number (approximately 2.718281828) such that the function ex equals its own derivative. The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. The exponents function is often written as exp(x), especially when the input is an expression too complex to be written as an exponents.( Source – Wikipedia)


The grade 7 math exponents solving problems are given below.


Example problems - grade 7 math exponents:


Example 1:

Multiply -6a2bc, 2a2b and` -1/4`

Solution:

 We have learn that to find the product of three numbers, we first multiply two of them and then multiply the product obtained by the thirdnumber. Thus

= (-6a2bc) (2a2b) `(-1/4)`

= [(-6a2bc) (2a2b)] `(-1/4)`

= [(- 6x2) (a2 a2) (b b) c] `(-1/4)`

= (-12a4 b2 c)` (-1/4) `

= [ (-12) `(-1/4)` ] a4 b2 c

= 3a4 b2 c

Note: 3 = -6 * 2 * `(-1/4)` and a4b2c = a2bc * a2b

(Since two negative number multiplied makes one affirmative or positive number)


Some more example problems of grade 7 math exponents:


Example 2:

Find the product of `(-3/2)` x2, 6x y, 5xyz2 and -4 verify the result for x="1," y="2," z="0.5

Solution:

The product as [`-3/2` 6 (x2  x) y] [5 (-4) xyz2]

= (-9x3y) (-20xyz2)

= [ -9 (-20)] (xx) (y  y)  z2

= 180 x4 * 6 * 5 * (-4) and x4y2z2 = xy xyz2

= let us verify the product for x = 1, y = 2 and z = 0.5

LHS = [`-3/2` * 12] * (6 * 1 * 2) * [5 * 1 * 2 * (0.5)2] * - 4

  = `-3/2` * 12 * 2.5 * (-4)

  = 180

RHS = 180(1)4 (2)2 (0.5)2

  = 180 4 0.25

  =180

 Thus, we observe that the coefficient of the product of two or more monomials is equal to the product of their coefficient and the variable part of the product is equal to the product of the variable in the givenmonomials.


Example 3:

Evaluate 1022

Solution:

1022 = (100+2)2

  = 1002 + 2 * 100 * 2 +22

  = 10000+400+4

  = 10404

The solution is 10404.