Question

use the properties of exponents to rewrite the expression. $(-7x^{4}y^{4})(-7xy^{4})$ \\(\bigcirc\\) a. $-49x^{4}y^{4}$ \\(\bigcirc\\) b. $49x^{4}y^{16}$ \\(\bigcirc\\) c. $-49x^{5}y^{8}$ \\(\bigcirc\\) d. $49x^{5}y^{8}$ reset selection

Explanation:

Step1: Multiply the coefficients

Multiply \(-7\) and \(-7\). We know that \((-7)\times(-7) = 49\).

Step2: Multiply the \(x\)-terms

Using the property of exponents \(a^m\times a^n=a^{m + n}\), for \(x^4\) and \(x\) (which is \(x^1\)), we have \(x^4\times x^1=x^{4 + 1}=x^5\).

Step3: Multiply the \(y\)-terms

Using the same property of exponents, for \(y^4\) and \(y^4\), we have \(y^4\times y^4=y^{4+4}=y^8\).

Step4: Combine the results

Combining the coefficient, \(x\)-term, and \(y\)-term, we get \(49x^5y^8\).

Answer:

D. \(49x^{5}y^{8}\)