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Constant, Coefficient, Exponents:

Multiplication: of (3x)

3x  = 3 is the multiplies, and x is the coefficient.

The terms are a number (3) is the constant of a base, and the alphabet (x) is considered variable

Exponent: x7(x)

It’s the small number that appears above to the right of a base (7) of (x) (x) (x) (x) (x) (x) (x)

a + b is Variables only. In this case the variable appears to have no exponent, then it has an exponent of 1: x1 = x

8m = 8 is the coefficient, and m is the base, so 1 will be the exponent. (8m1)

Like Terms or Unlike Terms:

Like Terms: if it has the same base and same exponents (2a2 and -6a2)

Unlike Terms: if exponents are different because of the base 7m and 7n (power of exponents is 1)

Also if the exponents have positive or negative it is unlike terms. (10 and -10)

Combination of Base and Exponents

Add or Subtract:                                                         Combination: Can or Cannot

1. 10k2 – 10k                                                                  cannot – different exponent (K2 – K)

2.   n + 19n                                                                     can (base is same) (n + n)

3.   8x-3 + (-8x3)                                                            cannot - different exponents (-3, +3)

4.  -11y2 + (-15z2)                                                         cannot – base is different (y, z)

5.  a5b4c2 – (-2a5b4c2)                                                  can (base & exponents are same)

Multiply same base with - coefficient/base/exponent: 2m3 and 5m5?

Multiply the coefficient (2)(5) = 10

Base – put um together m + m = m

Exponent  3 + 5 = 8

Answer: 10m8

Multiply different base with - coefficient/base/exponent: (8x2y3)and (-9x7)?

Multiply the coefficient (8)(-9) = -72 (+, - = -)

Base – put um together x + x + y =  x2x7y3

Exponent x 2+ x 7 = x9

Exponent of y3

Answer: -72x9y3

Different base for dividend and divisor

Like: (35g10) ÷ (5y4) =

First multiply the coefficient 35 ÷ 5 = 7

The base is unable to divide by the divisor – such as “G10” with the base of “Y4

Since the 10 is greater than 4 – the answer will be “Y”. both cannot be divisor.

Answer:  7g10/y4

Let’s try :

same base with different exponents:

(18a4b3) ÷ (-6ab5) =

Coefficient  is 18 ÷ -6 = -3

Base plus exponent of “a” = (a4 – a = a3)

Base plus exponent of “b” = (b3 – b5 = b2)

The answer will be (-3 a3 ÷ b2)

Minus the exponents if have the same base such as:

(16c7) ÷ (4c7)

(16c7) ÷ (4c7) = 4

C7 – c7 = c0

C ÷ c = 1

Answer:  4(1) = 4