Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression (-25x^(8))/(5x).(1 point)
To simplify the expression (-25x^(8))/(5x), we can apply the properties of exponents.
First, we can divide -25 by 5 to get -5.
Next, we can simplify the x terms by subtracting the exponents since we're dividing two monomial bases with the same base:
x^(8) / x = x^(8-1) = x^(7)
Therefore, the expression (-25x^(8))/(5x) simplifies to -5x^(7).
Use the properties of integer exponents to simplify the expression (-4a^(4)) (-2a^(2))
To simplify the expression (-4a^(4)) (-2a^(2)), we can apply the property of exponents that states when we multiply two monomials with the same base, we add their exponents.
(-4a^(4)) (-2a^(2)) = -4 * -2 * a^(4+2) = 8a^(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 simplify the expression (3x^(3)y^(-4))/(12x^(7)y^(4)), we can apply the properties of exponents.
First, we can divide the constants 3 and 12, which gives us 1/4.
Next, we can simplify the x terms by subtracting the exponents since we're dividing two monomial bases with the same base:
x^(3) / x^(7) = x^(3-7) = x^(-4)
Finally, we can simplify the y terms by subtracting the exponents as well:
y^(-4) / y^(4) = y^(-4-4) = y^(-8)
Therefore, the expression (3x^(3)y^(-4))/(12x^(7)y^(4)) simplifies to (1/4)x^(-4)y^(-8).
Apply the properties of integer exponents to simplify the algebraic expression (2xy^(3))* (x^(2)y)^(3)
To simplify the expression (2xy^(3))*(x^(2)y)^(3), we can apply the properties of exponents.
First, we can simplify the exponent of the term (x^(2)y) by multiplying the exponents:
(x^(2)y)^(3) = x^(2*3) * y^(1*3) = x^(6) * y^(3)
Next, we can simplify the expression by multiplying the two terms:
(2xy^(3))*(x^(2)y)^(3) = 2xy^(3) * (x^(6) * y^(3))
Now, we can use the property of exponents that states when we multiply two monomials with the same base, we add their exponents:
2xy^(3) * (x^(6) * y^(3)) = 2x * x^(6) * y^(3+3) * y^(3)
Simplifying further:
2xy^(3) * (x^(6) * y^(3+3) * y^(3)) = 2x * x^(6+1) * y^(3+3+3)
Finally, we simplify the exponents:
2x * x^(6+1) * y^(3+3+3) = 2x^(7) * y^(9)
Therefore, the expression (2xy^(3))*(x^(2)y)^(3) simplifies to 2x^(7)*y^(9).
Apply the properties of integer exponents to simplify the algebraic expression (2xy^(3)^(4)* (x^(2)y)^(3)
To simplify the expression (2xy^(3)^(4)* (x^(2)y)^(3), we need to clarify the placement of parentheses.
If the expression is (2xy^(3)^(4)) * (x^(2)y)^(3), then we can proceed with the simplification.
However, if the expression is 2xy^(3)^(4) * (x^(2)y)^(3), then we first need to simplify the y^(3)^(4) term before proceeding further.
Assuming the intended expression is (2xy^(3)^(4)) * (x^(2)y)^(3):
First, we simplify the exponent of the term y^(3)^(4):
y^(3)^(4) = y^(3*4) = y^(12)
Next, we can simplify the expression by multiplying the two terms:
(2xy^(3)^(4)) * (x^(2)y)^(3) = 2xy^(12) * (x^(2)y)^(3)
Now, we can use the property of exponents that states when we multiply two monomials with the same base, we add their exponents:
2xy^(12) * (x^(2)y)^(3) = 2xy^(12) * x^(2*3) * y^(1*3) = 2xy^(12) * x^(6) * y^(3)
Finally, we simplify the exponents:
2xy^(12) * x^(6) * y^(3) = 2x^(7) * y^(15)
Therefore, the expression (2xy^(3)^(4)) * (x^(2)y)^(3) simplifies to 2x^(7) * y^(15).