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1/216 is the equivalent expression for the given exponent [tex]6^{-3}[/tex].
An algebraic expression is a mathematical expression involving mathematical operations, variables, numbers, and mathematical quantities and combinations of them.
A negative exponent is the reciprocal of the same exponent with a positive value.
The reciprocal of any number is given by the fraction with the number as denominator and 1 as the numerator.
Here the given negative exponent is given by,
[tex]6^{-3}[/tex]
The exponent with positive value of the given negative exponent is given by [tex]6^3[/tex]
Reciprocal of the above exponent with positive value is given by,
[tex]\frac{1}{6^3}[/tex]
So now Calculating the negative exponent we have,
[tex]6^{-3} = \frac{1}{ {6}^{3} } = \frac{1}{216} [/tex]
Hence the equivalent expression for the given negative exponent is 1/216.
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