expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression -25x^8/5x

Answer 1

To simplify the expression $-25x^8/5x$ using the properties of exponents, we can follow these steps:

Step 1: Simplify the coefficients

First, simplify the numerical coefficients:

$$-25/5=-5$$

Step 2: Apply the properties of exponents

Next, we apply the property of exponents that states:

$$\frac{a^m}{a^n}=a^{m-n}$$

In our expression, we have $x^8$ in the numerator and $x$ (which is the same as $x^1$) in the denominator. We can simplify this as follows:

$$\frac{x^8}{x^1}=x^{8-1}=x^7$$

Step 3: Combine the simplified parts

Now we can combine the simplified coefficient and the simplified exponent:

$$-25x^8/5x=-5x^7$$

Final Expression

Thus, the simplified expression is:

$$\boxed{{\displaystyle -5x^7}}$$