Exponent Rules
This Exponent rule states 1 raised to any power is 1
What is Rules of 1
Is this a Rational Exponent or a Radical Expression 3√8
Rational Exponent
(−𝑥^ 2 − 2) + (2𝑥^ 2 + 1)
𝑥^ 2 − 1
Multiply (2x + 5)(x +1)
= 2x^2 + 7x + 5
(7x^2+8x+2)(8x^2+6x+5)
56x^4+106x
Any non-zero number raised to the power of zero equals 1
What is the Zero Rule
Is this a Rational Exponent or a Radical Expression.
3√(8)
Radical Expression
(2𝑥^ 2 + 3) − (3 − 4𝑥^ 2 )
6𝑥 ^2
Multiply (x + 4)(x + 3)
= x 2 + 7x + 12
(x + 2y)(3x − 4y + 5)
3x^2 + 2xy + 5x − 8y^2 + 10y
This Rule tells us any non-zero number raised to a negative power equals the reciprocal raised to the opposite positive power.
What is Negative Exponents
What is a Rational Exponent
What are expressions with exponents that are rational numbers
(7𝑥^ 3 + 9𝑥) − (3𝑥^ 3 + 2)
4𝑥 ^3 + 9𝑥 − 2
Multiply (x - 6)(x + 2)
x ^2 -4x -12
Find the product of 3x + 5y – 6z and – 5x
= -15x2 – 25xy + 30xz
When Multiplying two powers that have the same base you can add the exponents.
What is the Product Rule
What is a Radical Expression
A radical expression is defined as any expression containing a radical (√) symbol
(7𝑥 + 9) − (3𝑥 + 9)
4x
Multiply . (2x + 1)(2x + 1)
= 4x2 + 4x + 1
Multiply x – y – z by -8x2.
= -8x3 + 8x2y + 8x2z
You can divide two powers with the same base by subtracting exponents
What is the Quotient Rule
Evaluate the following expression and write the answer as a single number without exponents.
36 1/2
36 1/2 = 6
(−12𝑥^ 4 + 10𝑥 ^5 + 2𝑥 ^3 ) + (14𝑥^ 3 + 23𝑥^ 5 + 8𝑥^4
33𝑥^ 5 − 4𝑥^ 4 + 16𝑥^ 3
Multiply (y + 6)(3y + 2)
= 3y^ 2 + 20y + 12
Multiply 4p3 – 12pq + 9q2 by -3pq.
= 12p4q + 36p2q2 – 27pq3