To simplify the expression \((4x^4y^{-4})^3(x^7y^3)^2\), we can apply the properties of integer exponents. Here are the steps:
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Apply the power to each factor in the first term: \[ (4x^4y^{-4})^3 = 4^3 (x^4)^3 (y^{-4})^3 = 64x^{12}y^{-12} \]
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Apply the power to each factor in the second term: \[ (x^7y^3)^2 = (x^7)^2 (y^3)^2 = x^{14}y^6 \]
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Multiply the two results together: \[ (64x^{12}y^{-12})(x^{14}y^6) \]
When multiplying the terms, we add the exponents of the same bases: \[ = 64 \cdot x^{12+14} \cdot y^{-12+6} = 64x^{26}y^{-6} \]
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Rewrite the expression in a more conventional form with positive exponents: \[ = \frac{64x^{26}}{y^6} \]
Now, let's find the equivalent algebraic expression based on the provided options:
- \(4x^2y^{18}\)
- \(\frac{4}{x^2y^{18}}\)
- \(\frac{64}{x^2y^{18}}\)
- \(64x^{20}\)
- \(\frac{x^2y^{18}}{64}\)
Given the outcome we derived, \(\frac{64x^{26}}{y^6}\), none of the options seem to match. However, none of those match our final result of \(\frac{64x^{26}}{y^6}\).
Please make sure I am provided with the complete or correct choices or clarify if there are other options to choose from. The expression we worked out is: \(\frac{64x^{26}}{y^6}\).
0 answers