Question

use the properties of exponents to rewrite the expression. $(-8x^{3}y)(-9x^{2}y^{4})$
a. $72x^{6}y^{4}$
b. $-72x^{5}y^{5}$
c. $-72x^{3}y^{4}$
d. $72x^{5}y^{5}$
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Explanation:

Step1: Multiply the coefficients

Multiply \(-8\) and \(-9\). Since \((-8)\times(-9) = 72\).

Step2: Multiply the \(x\)-terms

Using the property of exponents \(a^m\times a^n=a^{m + n}\), for \(x^3\times x^2\), we have \(x^{3+2}=x^5\).

Step3: Multiply the \(y\)-terms

Using the same exponent property, for \(y\times y^4\) (note that \(y = y^1\)), we get \(y^{1 + 4}=y^5\).

Step4: Combine the results

Combine the coefficient, \(x\)-term, and \(y\)-term: \(72x^5y^5\).

Answer:

D. \(72x^{5}y^{5}\)