# Determine if a Polynomial (5x^-4y-7)(6x^(2y^12))

(5x-4y-7)(6x2y12)
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify the expression.
Simplify each term.
Rewrite the expression using the negative exponent rule b-n=1bn.
(51x4y-7)(6x2y12)
Combine 5 and 1×4.
(5x4y-7)(6x2y12)
Combine 5×4 and y.
(5yx4-7)(6x2y12)
(5yx4-7)(6x2y12)
Simplify by multiplying through.
Apply the distributive property.
5yx4(6x2y12)-7(6x2y12)
Simplify the expression.
Rewrite using the commutative property of multiplication.
65yx4x2y12-7(6x2y12)
Multiply 6 by -7.
65yx4x2y12-42x2y12
65yx4x2y12-42x2y12
65yx4x2y12-42x2y12
Simplify each term.
Multiply 65yx4.
Combine 6 and 5yx4.
6(5y)x4x2y12-42x2y12
Multiply 5 by 6.
30yx4x2y12-42x2y12
30yx4x2y12-42x2y12
Combine 30yx4 and x2y12.
30yx2y12x4-42x2y12
Cancel the common factor of x2y12 and x4.
Factor x4 out of 30yx2y12.
x4(30yx2y12-4)x4-42x2y12
Cancel the common factors.
Multiply by 1.
x4(30yx2y12-4)x4⋅1-42x2y12
Cancel the common factor.
x4(30yx2y12-4)x4⋅1-42x2y12
Rewrite the expression.
30yx2y12-41-42x2y12
Divide 30yx2y12-4 by 1.
30yx2y12-4-42x2y12
30yx2y12-4-42x2y12
30yx2y12-4-42x2y12
30yx2y12-4-42x2y12
30yx2y12-4-42x2y12
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Not a polynomial
Determine if a Polynomial (5x^-4y-7)(6x^(2y^12))

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