Which expressions are equivalent to (1)/(5)*(1)/(5)*(1)/(5)*(1)/(5)? Choose 2 answers: (A) (5^(-2))^(2) (B) (5^(-4))^(0) (C) (5^(1))/(5^(4)) (D) 5^(2)*5^(-6)

Understand Given Expression: Understand the given expression. The given expression is (1/5) * (1/5) * (1/5) * (1/5), which is the multiplication of the fraction 1/5 by itself four times.Simplify Expression: Simplify the given expression. When you multiply a fraction by itself, you multiply the numerators and the denominators separately. So, (1/5) * (1/5) * (1/5) * (1/5) = 1^4 / 5^4 = 1 / 5^4.Compare with Answer Choices: Compare the simplified expression with the answer choices. We have simplified the given expression to 1 / 5^4. Now we need to find which of the answer choices are equivalent to this expression. A) (5^(-2))^2 = 5^(-4) because when you raise a power to a power, you multiply the exponents. This is equivalent to 1 / 5^4. B) (5^(-4))^0 = 1 because any number (except 0) raised to the power of 0 is 1. This is not equivalent to 1 / 5^4. C) (5^(1))/(5^(4)) = 5^(-3) because when you divide powers with the same base, you subtract the exponents. This is not equivalent to 1 / 5^4. D) 5^(2)*5^(-6) = 5^(2-6) = 5^(-4) because when you multiply powers with the same base, you add the exponents. This is equivalent to 1 / 5^4.

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Which expressions are equivalent to
(1)/(5)*(1)/(5)*(1)/(5)*(1)/(5)?
Choose 2 answers:
(A) (5^(-2))^(2)
(B) (5^(-4))^(0)
(C) (5^(1))/(5^(4))
(D) 5^(2)*5^(-6)

Which expressions are equivalent to $\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} ?$ $\newline$ Choose $2$ answers: $\newline$ (A) $\left(5^{-2}\right)^{2}$ $\newline$ (B) $\left(5^{-4}\right)^{0}$ $\newline$ (C) $\frac{5^{1}}{5^{4}}$ $\newline$ (D) $5^{2} \cdot 5^{-6}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} ?

\newline

Choose

2

answers:

\newline

(A)

\left(5^{-2}\right)^{2}

\newline

(B)

\left(5^{-4}\right)^{0}

\newline

(C)

\frac{5^{1}}{5^{4}}

\newline

(D)

5^{2} \cdot 5^{-6}

Understand Given Expression: Understand the given expression. $\newline$ The given expression is $\frac{1}{5}$ * $\frac{1}{5}$ * $\frac{1}{5}$ * $\frac{1}{5}$ , which is the multiplication of the fraction $\frac{1}{5}$ by itself four times.
Simplify Expression: Simplify the given expression. $\newline$ When you multiply a fraction by itself, you multiply the numerators and the denominators separately. So, $(\frac{1}{5}) \times (\frac{1}{5}) \times (\frac{1}{5}) \times (\frac{1}{5}) = \frac{1^4}{5^4} = \frac{1}{5^4}$ .
Compare with Answer Choices: Compare the simplified expression with the answer choices. $\newline$ We have simplified the given expression to $1 / 5^4$ . Now we need to find which of the answer choices are equivalent to this expression. $\newline$ A) $(5^{-2})^2 = 5^{-4}$ because when you raise a power to a power, you multiply the exponents. This is equivalent to $1 / 5^4$ . $\newline$ B) $(5^{-4})^0 = 1$ because any number (except $0$ ) raised to the power of $0$ is $1$ . This is not equivalent to $1 / 5^4$ . $\newline$ C) $(5^{1})/(5^{4}) = 5^{-3}$ because when you divide powers with the same base, you subtract the exponents. This is not equivalent to $1 / 5^4$ . $\newline$ D) $(5^{-2})^2 = 5^{-4}$ $0$ because when you multiply powers with the same base, you add the exponents. This is equivalent to $1 / 5^4$ .