What is the exponent in the exponential form of the expression (1/8)(1/8)(1/8)

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1 answer

To express the product \( (1/8)(1/8)(1/8) \) in exponential form, we first recognize that multiplying \( \frac{1}{8} \) by itself three times can be represented as \( \left( \frac{1}{8} \right)^3 \).

Next, we can also rewrite \( \frac{1}{8} \) as \( 8^{-1} \). Therefore, we have:

\[ \frac{1}{8} = 8^{-1} \]

Now substituting into our expression:

\[ (1/8)(1/8)(1/8) = \left(8^{-1}\right) \left(8^{-1}\right) \left(8^{-1}\right) = 8^{-1} \times 8^{-1} \times 8^{-1} \]

Using the property of exponents that states \( a^m \times a^n = a^{m+n} \):

\[ 8^{-1} \times 8^{-1} \times 8^{-1} = 8^{-1 - 1 - 1} = 8^{-3} \]

Thus, the exponential form of the expression \( (1/8)(1/8)(1/8) \) is \( 8^{-3} \).

The exponent in this exponential form is:

\[ \boxed{-3} \]