Choose the four expressions that are equivalent to 3⁻⁴.
1) 1/81
2) 1/3⁴
3) 3¹ × 3⁻⁴
4) (3⁻⁷)³
5) (1/3)⁴
6) 3²/3⁶
Choose the four expressions that are equivalent to 3⁻⁴.
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To find the expressions equivalent to ( 3^{-4} ), we first recall that ( a^{-n} = frac{1}{a^n} ). This means that ( 3^{-4} = frac{1}{3^4} = frac{1}{81} ).
Now, let’s evaluate each expression:
1) ( frac{1}{81} ): This is ( 3^{-4} ), so it’s equivalent.
2) ( frac{1}{3^4} ): This is also ( 3^{-4} ), so it’s equivalent.
3) ( 3^{1} times 3^{-4} ): This simplifies to ( 3^{-3} ), which is not equivalent to ( 3^{-4} ).
4) ( (3^{-7})^3 ): This simplifies to ( 3^{-21} ), which is not equivalent to ( 3^{-4} ).
5) ( (1/3)^4 ): This is ( 3^{-4} ), so it’s equivalent.
6) ( frac{3^2}{3^6} ): This simplifies to ( 3^{-4} ), so it’s equivalent.
So, the four expressions that are equivalent to ( 3^{-4} ) are:
1) ( frac{1}{81} )
2) ( frac{1}{3