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Which expressions are equivalent to
5^(12)*5^(8) ?
Choose 2 answers:
A
25^(20)
B
(25^(5))^(4)
c.
(5^(3)*5^(2))^(4)
D
(5^(5))^(4)

Which expressions are equivalent to $\newline$ $5^{12} \cdot 5^{8}$ ? $\newline$ Choose $2$ answers: $\newline$ A $\newline$ $25^{20}$ $\newline$ B $\newline$ $(25^{5})^{4}$ $\newline$ C. $\newline$ $(5^{3} \cdot 5^{2})^{4}$ $\newline$ D $\newline$ $(5^{5})^{4}$

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Evaluate expressions using properties of exponents

Full solution

Q. Which expressions are equivalent to

\newline

5^{12} \cdot 5^{8}

?

\newline

Choose

2

answers:

\newline

A

\newline

25^{20}

\newline

B

\newline

(25^{5})^{4}

\newline

C.

\newline

(5^{3} \cdot 5^{2})^{4}

\newline

D

\newline

(5^{5})^{4}

Combine exponents using product rule: Combine the exponents of the same base using the product rule for exponents, which states that $a^m \cdot a^n = a^{m+n}$ when the base $a$ is the same. $\newline$ Calculation: $5^{12} \cdot 5^{8} = 5^{12+8} = 5^{20}$
Evaluate choice A: Evaluate each answer choice to see if it is equivalent to $5^{20}$ . $\newline$ A. $25^{20} = (5^2)^{20} = 5^{2\cdot20} = 5^{40}$ , which is not equal to $5^{20}$ .
Evaluate choice B: Evaluate choice B. $\newline$ B. $(25^{5})^{4} = ((5^{2})^{5})^{4} = (5^{2\cdot 5})^{4} = 5^{10\cdot 4} = 5^{40}$ , which is not equal to $5^{20}$ .
Evaluate choice C: Evaluate choice C. $\newline$ C. $(5^{3}\cdot5^{2})^{4} = (5^{3+2})^{4} = 5^{5\cdot4} = 5^{20}$ , which is equal to $5^{20}$ .
Evaluate choice D: Evaluate choice D. $\newline$ D. $(5^{5})^{4} = 5^{5\times4} = 5^{20}$ , which is equal to $5^{20}$ .

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