Answer:
Simplified form: [tex]\Rightarrow \dfrac{5x^{3}}{4y^{4}}[/tex]
Step-by-step explanation:
Given: Phrase " 15 x to the fifth power over 24 y to the eighth power divided by 4 x squared over 8 y to the fourth power"
Numerator: "15 x to the fifth power over 24 y to the eighth power"
[tex]\Rightarrow \dfrac{15x^5}{24y^8}[/tex]
Denominator: "4 x squared over 8 y to the fourth power"
[tex]\Rightarrow \dfrac{4x^2}{8y^4}[/tex]
Now we simplify numerator and denominator using exponent law.
Exponent Law:
[tex]a^m\cdot a^n=a^{m+n}[/tex]
[tex]a^m\div a^n=a^{m-n}[/tex]
[tex]\Rightarrow \dfrac{15x^5}{24y^8}\div \dfrac{4x^2}{8y^4}[/tex]
[tex]\Rightarrow \dfrac{15x^5}{24y^8}\times \dfrac{8y^4}{4x^2}[/tex]
[tex]\Rightarrow \dfrac{15x^5\cdot 8y^4}{24y^8\cdot 4x^2}[/tex]
[tex]\Rightarrow \dfrac{120x^5y^4}{96x^2y^8}[/tex]
[tex]\Rightarrow \dfrac{5x^{5-2}}{4y^{8-4}}[/tex]
[tex]\Rightarrow \dfrac{5x^{3}}{4y^{4}}[/tex]