Answer:
[tex]x^8\sqrt[3]{x}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{x^{25}}[/tex]
Apply the exponent rule [tex]a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies \sqrt[3]{x^{(24+1)}}=\sqrt[3]{x^{24}x^1}=\sqrt[3]{x^{24}x}[/tex]
Apply the radical rule [tex]\sqrt{ab} =\sqrt{a}\sqrt{b}[/tex]:
[tex]\implies =\sqrt[3]{x^{24}x}=\sqrt[3]{x^{24}}\sqrt[3]{x}[/tex]
Apply the radical rule [tex]\sqrt[a]{x^b} =x^{\frac{b}{a}}[/tex]:
[tex]\implies \sqrt[3]{x^{24}}\sqrt[3]{x}=x^{\frac{24}{3}}\sqrt[3]{x}=x^8\sqrt[3]{x}[/tex]
