1Cademy - Simplifying $$(5x^{-3})^2$$ and $$(8a^{-4})^2$$ Using Exponent Properties

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Product to a Power Property for Exponents

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Simplifying $(5x^{-3})^2$ and $(8a^{-4})^2$ Using Exponent Properties

Apply multiple exponent properties to simplify expressions where a product containing a negative exponent is raised to an outer power.

ⓐ $(5x^{-3})^2 = \frac{25}{x^6}$ : Use the Product to a Power Property to distribute the outer exponent: $5^2(x^{-3})^2$ . Apply the Power Property to multiply the exponents on the variable: $25x^{-6}$ . Use the negative exponent definition ( $a^{-n} = \frac{1}{a^n}$ ) to rewrite the expression with a positive exponent: $25 \cdot \frac{1}{x^6} = \frac{25}{x^6}$ .

ⓑ $(8a^{-4})^2 = \frac{64}{a^8}$ : Distribute the exponent: $8^2(a^{-4})^2$ . Multiply the variable's exponents: $64a^{-8}$ . Rewrite using the negative exponent definition: $64 \cdot \frac{1}{a^8} = \frac{64}{a^8}$ .

Updated 2026-05-13

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