Variables and Algebraic Expressions: Using powers

Let's break down the fraction's numerator into an expression:

$8x^2=4\times2\times x\times x$

And now the expression will be:

$\frac{4\times2\times x\times x}{4x}+3x=$

Let's reduce and get:

$2x+3x=5x$

We'll use the law of exponents for multiplication between terms with identical bases:

$a^m\cdot a^n=a^{m+n}$

We'll apply this law to the expression in the problem:

$2x^3\cdot x^2-3x\cdot x^4+6x\cdot x^2-7x^3\cdot 5=2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3$

When we apply the above law to the first three terms from the left, while remembering that any number can always be considered as that number raised to the power of 1:

$a=a^1$

And in the last term we performed the numerical multiplication,

We'll continue and simplify the expression we got in the last step:

$2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3=2x^5-3x^5+6x^3-35x^3=-x^5-29x^3$

Where in the first stage we simplified the expressions in the exponents of the terms in the expression and in the second stage we combined like terms,

Therefore the correct answer is answer A.

According to the laws of multiplication, we must first simplify everything into one exercise:

$\frac{9m\times3m}{3m^2\times6}=$

We will simplify and get:

$\frac{9m^2}{m^2\times6}=$

We will simplify and get:

$\frac{9}{6}=$

We will factor the expression into a multiplication:

$\frac{3\times3}{3\times2}=$

We will simplify and get:

$\frac{3}{2}=1.5$