To determine the expression that [tex]\(\left(x^3\right)^5\)[/tex] is equivalent to, we use the power rule of exponents. The power rule of exponents states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].
Let's break it down step-by-step:
1. Identify the base and the exponents: In the expression [tex]\(\left(x^3\right)^5\)[/tex], the base is [tex]\(x\)[/tex], the inner exponent is 3, and the outer exponent is 5.
2. Apply the power rule: Multiply the inner exponent by the outer exponent. So you would calculate [tex]\(3 \cdot 5\)[/tex].
3. Result of multiplication: [tex]\(3 \cdot 5 = 15\)[/tex].
4. Rewrite the expression: Substitute the new exponent back into the expression. [tex]\(\left(x^3\right)^5\)[/tex] becomes [tex]\(x^{15}\)[/tex].
Therefore, [tex]\(\left(x^3\right)^5\)[/tex] is equivalent to [tex]\(x^{15}\)[/tex].
