Question

1) 4x^5 y^7(-2xy^2)2) ( - 3x^5 y^2)^33) (-5x^4 y)^2​

Answer 1

1) -8x^6 y^9

2) -27x^15 y^6

3) 25x^8 y^2

Answer 2

Let's simplify each of the given expressions:

1. $4x^5y^7(-2xy^2)$

To simplify this expression, we multiply the coefficients and add the exponents of the variables with the same base.

$4 \cdot (-2) = -8$

For the variable $x$, we add the exponents: $5 + 1 = 6$

For the variable $y$, we add the exponents: $7 + 2 = 9$

Therefore, the simplified expression is $-8x^6y^9$.

2. $(-3x^5y^2)^3$

To simplify this expression, we raise the entire expression inside the parentheses to the power of 3.

$(-3x^5y^2)^3 = (-3)^3(x^5)^3(y^2)^3$

$(-3)^3 = -27$

$(x^5)^3 = x^{5 \cdot 3} = x^{15}$

$(y^2)^3 = y^{2 \cdot 3} = y^6$

Therefore, the simplified expression is $-27x^{15}y^6$.

3. $(-5x^4y)^2$

To simplify this expression, we square the entire expression inside the parentheses.

$(-5x^4y)^2 = (-5)^2(x^4)^2(y)^2$

$(-5)^2 = 25$

$(x^4)^2 = x^{4 \cdot 2} = x^8$

$(y)^2 = y^2$

Therefore, the simplified expression is $25x^8y^2$.

So, the simplified expressions are:

1. $-8x^6y^9$

2. $-27x^{15}y^6$

3. $25x^8y^2$