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)

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

Home

Math Problems

Grade 8

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

\newline

25^{20}

\newline

\newline

(25^{5})^{4}

\newline

\newline

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

\newline

\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 $5^{20}$ .