Simplify each expression, but don’t evaluate.
$\frac{(x^2{)}^4}{{\left(x^3\right)}^3}$

• A. $x^{\frac{8}{9}}$
• B. $x^{-1}$
• C. $x^1$
• D. $x^{\frac{1}{2}}$

Answer: (B)

Verified step by step guidance

1. Recall the Power Rule for Exponents, which states that when you raise a power to another power, you multiply the exponents: \(\left(a^{m}\right)^{n} = a^{m \times n}\).
2. Identify the base and the exponents in the given expression. For example, if the expression is \(\left(x^{3}\right)^{4}\), the base is \(x\), the first exponent is 3, and the second exponent is 4.
3. Apply the Power Rule by multiplying the exponents: multiply the first exponent by the second exponent, such as \$3 \times 4$.
4. Rewrite the expression with the base and the new exponent: \(x^{3 \times 4}\).
5. Simplify the exponent multiplication to get the final exponent form, but do not calculate the numerical value if the problem asks to stop before final evaluation.