Certainly! Let's simplify the given expression step-by-step.
We need to simplify the expression \(\left(x^7\right)^6\).
1. Identify the base and the exponents: In the expression \(\left(x^7\right)^6\), the base is \(x\). The inner exponent is \(7\) (from \(x^7\)) and the outer exponent is \(6\) (from the outside parentheses).
2. Apply the power rule: The power rule of exponents states that [tex]\[\left(a^m\right)^n = a^{m \cdot n}\][/tex]. Here, \(a\) is the base, and \(m\) and \(n\) are the exponents.
3. Multiply the exponents: Using the power rule, we multiply the inner exponent by the outer exponent:
[tex]\[
\left(x^7\right)^6 = x^{7 \cdot 6}
\][/tex]
4. Calculate the multiplication: Perform the multiplication of the exponents:
[tex]\[
7 \cdot 6 = 42
\][/tex]
5. Write the simplified expression: Now, substitute the calculated exponent back in:
[tex]\[
\left(x^7\right)^6 = x^{42}
\][/tex]
So, the simplified form of the expression [tex]\(\left(x^7\right)^6\)[/tex] is [tex]\(x^{42}\)[/tex].
