We have the next expression:
[tex]5^5(16^2\cdot5^3)^3[/tex]
Now, solve the parentheses using the next property:
[tex](a^m)^n=a^{m\cdot n}[/tex]
Therefore:
[tex](16^2\cdot5^3)^3=16^{2\cdot3}\cdot5^{3\cdot3}[/tex][tex]=16^6\cdot5^9[/tex]
Which represents the product of two powers.
But, we need to find two quotients:
Then, we can rewrite the next expression:
[tex]16^6=16^4\cdot16^2[/tex]
To make fractions, we use the next property:
[tex]a^m=\frac{1}{a^{-m}}[/tex]
Then:
[tex]16^416^2=\frac{1}{16^{-4}16-^2}[/tex]
The result expression for the product of two powers:
[tex]\frac{5^2\cdot5^9}{16^{-4}16-^2}[/tex]
The result for the product of two quotients:
[tex]\frac{16^4\cdot5^9}{16^{-2}\cdot5^{-2}}[/tex]
