Which expressions are equivalent to (4^(-3))/(4^(-1)) ? Choose 2 answers: (A) (4^(1))/(4^(3)) (B) (1)/(4^(2)) c. 4^(3)*4^(1) D (4^(-1))^(-3)

Simplify Exponential Expression: Simplify the given expression using the properties of exponents. When dividing exponential expressions with the same base, subtract the exponents. (4^(-3))/(4^(-1)) = 4^(-3 - (-1)) = 4^(-3 + 1) = 4^(-2)Compare with Options: Compare the simplified expression with the given options. We have simplified the expression to 4^(-2). Now we need to see which options are equivalent to this expression. Option (A) (4^(1))/(4^(3)) simplifies to 4^(1-3) = 4^(-2). Option (B) (1)/(4^(2)) is already in the form 4^(-2). Option (C) 4^(3)*4^(1) simplifies to 4^(3+1) = 4^(4), which is not equivalent. Option (D) (4^(-1))^(-3) simplifies to 4^(-1 * -3) = 4^(3), which is not equivalent.Identify Correct Options: Identify the correct options. From Step 2, we can see that Option (A) and Option (B) are equivalent to the simplified expression 4^(-2).

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Which expressions are equivalent to
(4^(-3))/(4^(-1)) ?
Choose 2 answers:
(A)
(4^(1))/(4^(3))
(B)
(1)/(4^(2))
c.
4^(3)*4^(1)
D
(4^(-1))^(-3)

Which expressions are equivalent to $\frac{4^{-3}}{4^{-1}}$ ? $\newline$ Choose $2$ answers: $\newline$ (A) $\frac{4^{1}}{4^{3}}$ $\newline$ (B) $\frac{1}{4^{2}}$ $\newline$ c. $4^{3} \cdot 4^{1}$ $\newline$ D $\left(4^{-1}\right)^{-3}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

\frac{4^{-3}}{4^{-1}}

\newline

Choose

2

answers:

\newline

(A)

\frac{4^{1}}{4^{3}}

\newline

(B)

\frac{1}{4^{2}}

\newline

4^{3} \cdot 4^{1}

\newline

\left(4^{-1}\right)^{-3}

Simplify Exponential Expression: Simplify the given expression using the properties of exponents. $\newline$ When dividing exponential expressions with the same base, subtract the exponents. $\newline$ $(4^{-3})/(4^{-1}) = 4^{-3 - (-1)} = 4^{-3 + 1} = 4^{-2}$
Compare with Options: Compare the simplified expression with the given options. $\newline$ We have simplified the expression to $4^{-2}$ . Now we need to see which options are equivalent to this expression. $\newline$ Option (A) $(4^{1})/(4^{3})$ simplifies to $4^{1-3} = 4^{-2}$ . $\newline$ Option (B) $(1)/(4^{2})$ is already in the form $4^{-2}$ . $\newline$ Option (C) $4^{3}*4^{1}$ simplifies to $4^{3+1} = 4^{4}$ , which is not equivalent. $\newline$ Option (D) $(4^{-1})^{(-3)}$ simplifies to $4^{-1 * -3} = 4^{3}$ , which is not equivalent.
Identify Correct Options: Identify the correct options. $\newline$ From Step $2$ , we can see that Option (A) and Option (B) are equivalent to the simplified expression $4^{-2}$ .