Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x4y−4)3(x7y3)2 .(1 point)
To generate an equivalent algebraic expression, we will need to apply the properties of integer exponents. Let's break down the given expression:
(4x^4y^(-4))^3 * (x^7y^3)^2
We can simplify each part of the expression using the properties of exponents:
First, let's simplify (4x^4y^(-4))^3. To raise a power to a power, we multiply the exponents:
(4^3) * (x^(4*3)) * (y^(-4 * 3))
= 64x^12 * y^(-12)
Next, let's simplify (x^7y^3)^2. To raise a power to a power, we multiply the exponents:
(x^(7*2)) * (y^(3*2))
= x^14 * y^6
Now, we can combine the simplified parts of the expression:
64x^12 * y^(-12) * x^14 * y^6
To multiply variables with the same base, we add their exponents:
64 * x^(12+14) * y^(-12+6)
= 64x^26 * y^(-6)
Therefore, the equivalent algebraic expression is 64x^26 * y^(-6).
To generate an equivalent algebraic expression, we can use the properties of integer exponents.
The property we need to apply is that when we raise a power to another power, we need to multiply the exponents.
Let's break down the given expression step by step:
(4x^4y^−4)^3 * (x^7y^3)^2
First, let's simplify the exponents of the first term:
(4^3 * x^(4*3) * y^((-4)*3)) * (x^7y^3)^2
Simplifying further:
(64 * x^12 * y^(-12)) * (x^14 * y^6)
Now, let's simplify the exponents of the second term:
64 * x^(12+14) * y^(-12+6)
Simplifying the exponents even further:
64 * x^26 * y^(-6)
Therefore, the equivalent algebraic expression to (4x^4y^−4)^3 * (x^7y^3)^2 is 64x^26 y^−6.