1. **State the problem:** We want to express $\left(5\sqrt{26}\right)^9$ in the form $26^h$ and find the value of $h$. 2. **Rewrite the expression:** Recall that $\sqrt{26} = 26^{\frac{1}{2}}$, so $$\left(5\sqrt{26}\right)^9 = \left(5 \times 26^{\frac{1}{2}}\right)^9.$$ 3. **Apply exponent rules:** Using the property $(ab)^n = a^n b^n$, we get $$5^9 \times \left(26^{\frac{1}{2}}\right)^9 = 5^9 \times 26^{\frac{9}{2}}.$$ 4. **Express in terms of $26^h$ only:** We want to write the entire expression as $26^h$. Notice $5^9$ is not a power of 26, so we need to check if $5^9$ can be expressed as $26^k$ for some $k$. Since 5 and 26 are not powers of each other, this is not possible. 5. **Conclusion:** The expression cannot be written purely as $26^h$ because of the factor $5^9$. However, if the problem intends to write only the $\sqrt{26}$ part raised to the 9th power as $26^h$, then $$\left(\sqrt{26}\right)^9 = 26^{\frac{9}{2}} = 26^{4.5}.$$ **Final answer:** $h = \frac{9}{2}$ or $4.5$ if considering only the $\sqrt{26}$ part. If the entire expression $\left(5\sqrt{26}\right)^9$ must be expressed as $26^h$, it is not possible due to the factor $5^9$.