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 4^{-3} 4^{-1} ? Choose 2 answers:
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To simplify the expression ( 4^{-3} 4^{-1} ), we can use the property of exponents that states ( a^m cdot a^n = a^{m+n} ).
1. Combine the exponents:
[
4^{-3} cdot 4^{-1} = 4^{-3 + (-1)} = 4^{-4}
]
Now, let’s check each option to find equivalent expressions to ( 4^{-4} ):
A. ( frac{4^{1}}{4^{3}} ):
[
frac{4^{1}}{4^{3}} = 4^{1-3} = 4^{-2} quad (text{Not equivalent})
]
B. ( frac{1}{4^{2}} ):
[
frac{1}{4^{2}} = 4^{-2} quad (text{Not equivalent})
]
C. ( 4^{3} cdot 4^{1} ):
[
4^{3} cdot 4^{1} = 4^{3+1} = 4^{4} quad (text{Not equivalent to } 4^{-4})
]
D. ( (4^{-1})^{-3} ):
[
(4^{-1})^{-3}