Question

use the properties of exponents to rewrite the expression. $(-8x^{2}y^{3})(-5x^{2}y^{3})$
a. $40x^{4}y^{6}$
b. $40x^{4}y^{9}$
c. $-40x^{4}y^{6}$
d. $-40x^{2}y^{3}$
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Explanation:

Step1: Multiply the coefficients

Multiply \(-8\) and \(-5\). Since \((-8)\times(-5) = 40\).

Step2: Multiply the \(x\)-terms

Use the property of exponents \(a^m\times a^n=a^{m + n}\). For \(x^2\times x^2\), we have \(x^{2+2}=x^4\).

Step3: Multiply the \(y\)-terms

Using the same exponent property, for \(y^3\times y^3\), we get \(y^{3 + 3}=y^6\).

Step4: Combine the results

Combine the coefficient, \(x\)-term, and \(y\)-term: \(40x^4y^6\).

Answer:

A. \(40x^{4}y^{6}\)