Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8/5x
To simplify the expression, we can apply the properties of exponents.
First, let's simplify the numerical coefficient: -25/5 = -5.
Next, we can simplify the variable bases: x^8 / x^1 = x^(8-1) = x^7.
Therefore, the simplified expression is -5x^7.
Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2)
To simplify the expression, we can apply the properties of exponents.
Using the product of powers property, we can multiply the coefficients (−4)(−2) = 8.
Then, using the power of a power property, we can multiply the variables a^4 * a^2 = a^(4+2) = a^6.
Therefore, the simplified expression is 8a^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3 y−^4/12x^7 y^4
To generate an equivalent algebraic expression, we can apply the properties of exponents.
First, let's simplify the numerical coefficients: 3/12 = 1/4.
Next, let's simplify the variables with the same base, x: x^3 / x^7 = x^(3-7) = x^(-4).
Similarly, for the variables with the same base, y: y^(-4) / y^4 = y^(-4-4) = y^(-8).
Thus, the equivalent algebraic expression is (1/4) * (x^(-4)) * (y^(-8)), or simply (1/4x^4y^8).
Apply the properties of integer exponents to simplify the algebraic expression (2xy^3)^4 ⋅ (x^2y)^3
To simplify the algebraic expression, we can apply the properties of exponents.
First, let's simplify the expression within parentheses:
(2xy^3)^4 = 2^4 * (x^1)^4 * (y^3)^4 = 16x^4y^12.
Similarly, (x^2y)^3 = (x^2)^3 * (y^1)^3 = x^6y^3.
Next, we can simplify the expression by multiplying the exponents:
16x^4y^12 * x^6y^3 = 16x^(4+6)y^(12+3) = 16x^10y^15.
Therefore, the simplified algebraic expression is 16x^10y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a^3 b^4 c^−2/3a^−4 b^0 c^3)^−2
To simplify the algebraic expression, we can apply the properties of exponents.
First, let's simplify the expression within parentheses:
(-5a^3 b^4 c^(-2))/(3a^(-4) b^0 c^3).
Next, apply the negative exponent property:
(-5 * a^3 * b^4 * c^(-2))/(3 * a^(-4) * b^0 * c^3).
Simplify the coefficients:
(-5 * 1 * 1 * 1)/(3 * 1 * 1 * 1) = -5/3.
Now, simplify the variables with the same base:
a^3 / a^(-4) = a^3 * a^4 = a^(3+4) = a^7.
b^4 / b^0 = b^4 * b^(-0) = b^4 * 1 = b^4.
c^(-2) / c^3 = c^(-2) * c^(-3) = c^(-2-3) = c^(-5) = 1/c^5.
Putting it all together, the simplified expression is:
(-5/3) * a^7 * b^4 * (1/c^5) = -5a^7b^4 / (3c^5).
Which historical documents help shape the colonist's views of government?(1 point)
Responses
A. Magna Carta, Iroquois Constitution, Common Sense
B. Magna Carta, Mayflower Compact, Common Sense
C. Virginia Declaration of Rights, Common Sense, Bill of Rights
D. Common Sense, Articles of Confederation, Declaration of the Rights of Man