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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: x^{7}(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: x^{1 }= x
8m = 8 is the coefficient, and m is the base, so 1 will be the exponent. (8m^{1)}
^{ }
Like Terms or Unlike Terms:
Like Terms: if it has the same base and same exponents (2a^{2 }and 6a^{2)}
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. 10k^{2} – 10k cannot – different exponent (K^{2} – K)
2. n + 19n can (base is same) (n + n)
3. 8x^{3} + (8x^{3}) cannot  different exponents (3, +3)
4. 11y^{2} + (15z2) cannot – base is different (y, z)
5. a^{5}b^{4}c^{2} – (2a^{5}b^{4}c^{2}) can (base & exponents are same)
Multiply same base with  coefficient/base/exponent: 2m^{3 }and 5m^{5}?
Multiply the coefficient (2)(5) = 10
Base – put um together m + m = m
Exponent 3 + 5 = 8
Answer: 10m^{8}
Multiply different base with  coefficient/base/exponent: (8x^{2}y^{3})and (9x^{7})?
Multiply the coefficient (8)(9) = 72 (+,  = )
Base – put um together x + x + y = ^{ x2x7y3}
Exponent x ^{2}+ x ^{7} = x^{9}
Exponent of y^{3}
Answer: 72x^{9}y3
Different base for dividend and divisor
Like: (35g^{10}) ÷ (5y^{4}) =
First multiply the coefficient 35 ÷ 5 = 7
The base is unable to divide by the divisor – such as “G^{10}” with the base of “Y^{4}”
Since the 10 is greater than 4 – the answer will be “Y”. both cannot be divisor.
Answer: 7g^{10}/y^{4}
Let’s try :
same base with different exponents:
(18a^{4}b^{3}) ÷ (6ab^{5}) =
Coefficient is 18 ÷ 6 = 3
Base plus exponent of “a” = (a^{4} – a = a^{3})
Base plus exponent of “b” = (b^{3} – b^{5} = b^{2})
The answer will be (3 a^{3} ÷ b^{2})
Minus the exponents if have the same base such as:
(16c^{7}) ÷ (4c^{7})
(16c^{7}) ÷ (4c^{7}) = 4
C^{7} – c^{7} = c^{0}
C ÷ c = 1
Answer: 4(1) = 4