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5^5(16^2*5^3)^3=?Rewrite the expression as a product of two powers and two quotients

5^5(16^2*5^3)^3=?Rewrite the expression as a product of two powers and two quotients-example-1
User Reconbot
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We have the next expression:


5^5(16^2\cdot5^3)^3

Now, solve the parentheses using the next property:


(a^m)^n=a^(m\cdot n)

Therefore:


(16^2\cdot5^3)^3=16^(2\cdot3)\cdot5^(3\cdot3)
=16^6\cdot5^9

Which represents the product of two powers.

But, we need to find two quotients:

Then, we can rewrite the next expression:


16^6=16^4\cdot16^2

To make fractions, we use the next property:


a^m=(1)/(a^(-m))

Then:


16^416^2=(1)/(16^(-4)16-^2)

The result expression for the product of two powers:


(5^2\cdot5^9)/(16^(-4)16-^2)

The result for the product of two quotients:


(16^4\cdot5^9)/(16^(-2)\cdot5^(-2))

User Dipu
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