Sure! Let's simplify the given expression step-by-step.
We start with the expression:
[tex]\[
\frac{x^6}{x^5}
\][/tex]
To simplify this, we need to use the properties of exponents. One of the fundamental properties of exponents states that when we divide two expressions with the same base, we subtract the exponent of the denominator from the exponent of the numerator. Mathematically, this property is expressed as:
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
Here, the base [tex]\( a \)[/tex] is [tex]\( x \)[/tex], the exponent [tex]\( m \)[/tex] is [tex]\( 6 \)[/tex], and the exponent [tex]\( n \)[/tex] is [tex]\( 5 \)[/tex]. So, we apply this property:
[tex]\[
\frac{x^6}{x^5} = x^{6-5}
\][/tex]
Now, we perform the subtraction in the exponent:
[tex]\[
x^{6-5} = x^1
\][/tex]
By convention, any number or variable raised to the power of 1 is simply the number or variable itself, so:
[tex]\[
x^1 = x
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{x^6}{x^5}\)[/tex] is:
[tex]\[
x
\][/tex]
Therefore, the expression simplifies to:
[tex]\[
\boxed{x}
\][/tex]
