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 using quotient rule: Simplify the expression using the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. (4^(-3))/(4^(-1)) = 4^(-3 - (-1)) = 4^(-3 + 1) = 4^(-2)Check answer choices: Check each answer choice to see if it simplifies to 4^(-2). A) (4^(1))/(4^(3)) = 4^(1-3) = 4^(-2) This matches our simplified expression from Step 1.Continue checking: Continue checking the other answer choices. B) (1)/(4^(2)) = 4^0 / 4^2 = 4^(0-2) = 4^(-2) This also matches our simplified expression from Step 1.Check remaining choices: Check the remaining answer choices. C) 4^(3)*4^(1) = 4^(3+1) = 4^(4) This does not match our simplified expression from Step 1.Check last choice: Check the last answer choice. D) (4^(-1))^(-3) = 4^(-1 * -3) = 4^(3) This does not match our simplified expression from Step 1.

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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

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

\newline

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

\newline

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

\newline

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

Simplify using quotient rule: Simplify the expression using the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. $(4^{-3})/(4^{-1}) = 4^{-3 - (-1)} = 4^{-3 + 1} = 4^{-2}$
Check answer choices: Check each answer choice to see if it simplifies to $4^{-2}$ .
A) $(4^{1})/(4^{3}) = 4^{1-3} = 4^{-2}$
This matches our simplified expression from Step $1$ .
Continue checking: Continue checking the other answer choices. $\newline$ B) $(1)/(4^{2}) = 4^{0} / 4^{2} = 4^{(0-2)} = 4^{-2}$ $\newline$ This also matches our simplified expression from Step $1$ .
Check remaining choices: Check the remaining answer choices. $\newline$ C) $4^{3}\times4^{1} = 4^{3+1} = 4^{4}$ $\newline$ This does not match our simplified expression from Step $1$ .
Check last choice: Check the last answer choice. $\newline$ D) $(4^{-1})^{-3} = 4^{-1 \times -3} = 4^{3}$ $\newline$ This does not match our simplified expression from Step $1$ .