QuestionSimplify the expression: $(-2 x^{2} y^{3})^{4}(3.5 x^{0} y)(-2 x^{8} y^{12})(3.5 y)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(- x^{} y^{3}\right)^{4}\left(3.5 x^{0} y\right)$ . We need to simplify this expression3. We will use the rules of exponents and multiplication to simplify the expression

STEP 2

First, we need to simplify the expression inside the parentheses and raise it to the power of4. $\left(-2 x^{2} y^{}\right)^{4}$

STEP 3

The power of a product is the product of the powers. So, we can rewrite the expression as follows $(-2)^{} \cdot (x^{2})^{} \cdot (y^{3})^{}$

STEP 4

Calculate the value of $(-2)^{4}$ , and simplify the exponents by multiplying them with4.
$(-2)^{4} =16$ $(x^{2})^{4} = x^{8}$ $(y^{3})^{4} = y^{12}$

STEP 5

Now, we have the simplified form of the first part of the expression $16x^{8}y^{12}$

STEP 6

Next, we simplify the second part of the expression $\left(3.5 x^{0} y\right)$ .

STEP 7

Remember that any number raised to the power of0 is1. So, $x^{0} =1$ .
$3.5 \cdot1 \cdot y =3.5y$

STEP 8

Now, we multiply the two parts of the expression together $16x^{8}y^{12} \cdot3.5y$

STEP 9

We can simplify this by multiplying the coefficients and adding the exponents of $y$ .
$16 \cdot3.5 \cdot x^{8} \cdot y^{12} \cdot y$

STEP 10

Calculate the product of the coefficients and add the exponents of $y$ .
$56x^{8}y^{13}$ So, the simplified form of the given expression is $56x^{8}y^{13}$ .

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