Sure, let's simplify the given expression step by step.
We have:
[tex]\[
\frac{x^7}{x^4}
\][/tex]
To simplify this, we use the laws of exponents. One such law states that when you divide two expressions with the same base, you subtract the exponents. Mathematically, this law is expressed as:
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
In our expression, the base \(x\) is the same in both the numerator and the denominator. Therefore, we apply the rule to the exponents:
[tex]\[
\frac{x^7}{x^4} = x^{7-4}
\][/tex]
Next, we perform the subtraction in the exponent:
[tex]\[
7 - 4 = 3
\][/tex]
Thus, we can write:
[tex]\[
x^{7-4} = x^3
\][/tex]
Hence, the simplified form of \(\frac{x^7}{x^4}\) is:
[tex]\[
x^3
\][/tex]
Therefore, the exponent is:
[tex]\[
3
\][/tex]
