In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

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Rewrite the given expression: \((3x^{-4}y z^{-7})(3x)^{-3}\). Start by separating the terms and grouping the coefficients and variables for clarity.

Apply the property of exponents \(a^m a^n = a^{m+n}\) to combine like bases. For the base \(3\), combine \(3\) from the first term and \(3^{-3}\) from the second term.

For the variable \(x\), combine the exponents \(-4\) from the first term and \(-3\) from the second term using the same property of exponents.

The variables \(y\) and \(z\) are not present in the second term, so their exponents remain unchanged. Specifically, \(y\) has an exponent of \(1\), and \(z\) has an exponent of \(-7\).

Simplify the resulting expression by combining all terms and writing the final expression in simplified form, ensuring all exponents are combined correctly.

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