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Chapter 5: Problem 30

Find each product. $$\left(7 x^{4} y^{5}\right)\left(-10 x^{7} y^{11}\right)$$

Short Answer

Expert verified
The product of the two terms \(\left(7 x^{4} y^{5}\right)\left(-10 x^{7} y^{11}\right)\) is \(-70x^{11}y^{16}\).

Step by step solution

01

Multiplication of Coefficients

Multiply the numerical coefficient of first term (which is 7) by the coefficient of the second term (which is -10), resulting in \(7 \times (-10) = -70\).
02

Multiplication of x Terms

Next, multiply \(x^{4}\) by \(x^{7}\) , applying the rule of exponents which states that when multiplying terms with the same base, the exponents should be added. Therefore we have \(x^{4+7}=x^{11}\).
03

Multiplication of y Terms

Similarly, multiply \(y^{5}\) by \(y^{11}\), applying the same rule of exponents, resulting in \(y^{5+11}=y^{16}\).
04

Combine the Results

Combine the results of the above operations to find the final product. Therefore the product is -70, \(x^{11}\) times \(y^{16}\) which give us \(-70x^{11}y^{16}\).

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