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