Example

Simplifying (6k3)2(6k^3)^{-2} and (2b3)4(2b^3)^{-4} Using Exponent Properties

Apply the Product to a Power Property, the Power Property, and the definition of a negative exponent to simplify products raised to a negative power.

(6k3)2=136k6(6k^3)^{-2} = \frac{1}{36k^6}: Distribute the negative exponent to both factors in the base: 62(k3)26^{-2}(k^3)^{-2}. Apply the Power Property to multiply the exponents on the variable: 62k66^{-2}k^{-6}. Use the negative exponent definition, an=1ana^{-n} = \frac{1}{a^n}, to rewrite with positive exponents: 1621k6\frac{1}{6^2} \cdot \frac{1}{k^6}. Finally, simplify the numerical power: 136k6\frac{1}{36k^6}.

(2b3)4=116b12(2b^3)^{-4} = \frac{1}{16b^{12}}: Distribute the exponent: 24(b3)42^{-4}(b^3)^{-4}. Multiply the variable's exponents: 24b122^{-4}b^{-12}. Rewrite with positive exponents: 1241b12\frac{1}{2^4} \cdot \frac{1}{b^{12}}. Simplify the coefficient: 116b12\frac{1}{16b^{12}}.

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Updated 2026-04-29

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