To simplify the expression [tex]\((h^5)^9\)[/tex], we will use the power of a power rule in exponents. Here's a detailed, step-by-step solution:
1. Identify the structure of the expression:
- We start with the expression [tex]\((h^5)^9\)[/tex].
2. Use the power of a power rule:
- According to the power of a power rule: [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].
- In this case, the base [tex]\(a\)[/tex] is [tex]\(h\)[/tex], the first exponent [tex]\(m\)[/tex] is 5, and the second exponent [tex]\(n\)[/tex] is 9.
3. Multiply the exponents:
- We need to multiply the exponents 5 and 9.
- [tex]\(5 \times 9 = 45\)[/tex].
4. Rewrite the expression with the new exponent:
- Substitute the product of the exponents back into the expression.
- [tex]\((h^5)^9 = h^{45}\)[/tex].
Therefore, the simplified form of the expression [tex]\((h^5)^9\)[/tex] is [tex]\(h^{45}\)[/tex].
