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Rewrite each expression of two powers or a quotient of two powers

Rewrite each expression of two powers or a quotient of two powers-example-1

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Expression:


((8^4\cdot5^3)/(8^5))^2

To solve this expression first we have to use the Power rule:


(a^x)^y=a^(x\cdot y)

We can use this to simplify our expression as follows:


=((8^4)^2\cdot(5^3)^2)/((8^5)^2)
=(8^(4\cdot2)\cdot5^(3\cdot2))/(8^(5\cdot2))
=(8^8\cdot5^6)/(8^(10))

Now we will use the Quotient rule:


(a^x)/(a^y)=a^(x-y)

To do that, we have to have the same number a, we cannot do this in the division of 5^6/8^10, but we can use it in 8^8/8^10:


=(8^8)/(8^(10))\cdot5^6
=8^(8-10)\cdot5^6
=8^(-2)\cdot5^6

Answer:


=8^(-2)\cdot5^6

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