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Which expressions are equivalent to 512â‹…585^{12}\cdot 5^8512â‹…585, start superscript, 12, end superscript, dot, 5, start superscript, 8, end superscript?
Choose 2 answers:
Choose 2 answers:

(Choice A)
A
252025^{20}252025, start superscript, 20, end superscript
(Choice B)
B
(255)4\left( 25^{5} \right)^{4}(255)4left parenthesis, 25, start superscript, 5, end superscript, right parenthesis, start superscript, 4, end superscript
(Choice C)
C
(53â‹…52)4\left( 5^3 \cdot 5^2 \right)^{4}(53â‹…52)4left parenthesis, 5, cubed, dot, 5, squared, right parenthesis, start superscript, 4, end superscript
(Choice D)
D
(55)4(5^5)^4(55)4left parenthesis, 5, start superscript, 5, end superscript, right parenthesis, start superscript, 4, end superscript

Which expressions are equivalent to 51258512cdot 58512585 start superscript 12 end superscript dot 5 start superscript 8 end superscript Choose 2 answers Choose class=

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we conclude that the equivalent expression is the last one, we have:

5^12*5^8= (5^4)^5

Which expressions are equivalent to 5^12*5^8?

Here we need to use the exponent property:

x^a*x^b = x^{a + b)

Also, we have the property:

(x^a)^b = x^(a*b)

Now we can use the first property in our expression:

5^12*5^8 = 5^(12 + 8) = 5^20

Now, we can rewrite that:

5^20 = 5^(4*5) = (5^4)^5

Then we conclude that the equivalent expression is the last one, we have:

5^12*5^8= (5^4)^5

If you want to learn more about equivalent expressions:

https://brainly.com/question/2972832

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