Which expression is equivalent to (1/8)⁻⁶ ⋅ (1/8)³?
(1/8)⁻²
(1/8)⁻³
(1/16)⁻¹⁸
(1/16)⁻³
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Which expression is equivalent to (1/8)⁻⁶ ⋅ (1/8)³?
(1/8)⁻²
(1/8)⁻³
(1/16)⁻¹⁸
(1/16)⁻³
To solve the expression ((1/8)^{-6} cdot (1/8)^{3}), we can use the property of exponents that states when multiplying two expressions with the same base, we can add the exponents:
[
(1/8)^{-6} cdot (1/8)^{3} = (1/8)^{-6 + 3} = (1/8)^{-3}
]
Now, to express ((1/8)^{-3}) in another form, we can rewrite it as:
[
(1/8)^{-3} = (8)^{3} = 8^{3} = 512
]
However, for the sake of answering your multiple-choice question, we need to express it in a format consistent with your options. We know that:
[
(1/8)^{-3} = (1/8)^{-3}
]
This is equivalent to:
[
1 / (1/8)^{3} = 8^{3} = 512
]
To see if there’s a closer match among your options:
– None of the exact options listed match ((1/8)^{-3}) directly.
However, we can check which one corresponds to this expression. Since ((1/8)^{-3}) might be transformed, we see that:
[
(1/8)^{-3} =