Chapter 8.2, Problem 47STP

To determine

To simplify: The product of two monomials and to tell the exponent.

Answer to Problem 47STP

The simplified expression $8x^3\cdot \left(2x^2\right)=16\cdot x^5$ , so the exponent of the product is 5.

Explanation of Solution

Given information:

The product of two monomials is $8x^3\left(2x^2\right)$

Formula used:

The exponents are added in the multiplication of two monomials of same variables as $a^m\cdot a^n=a^{m+n}$ . Thus, the exponent of resultant is the sum of the exponents of monomials.

Calculations:

The two monomials are $8x^3$ and $2x^2$ .

  $\Rightarrow 8x^3\cdot 2x^2=\left(8\cdot 2\right)\cdot \left(x^3{x}^2\right)$

  $\Rightarrow 8x^3\cdot 2x^2=\left(16\right)\cdot \left(x^{3+2}\right)$

  $\Rightarrow 8x^3\cdot 2x^2=16\cdot x^5$

Thus, the simplified expression $8x^3\cdot \left(2x^2\right)=16\cdot x^5$ , so the exponent of product is 5.

Conclusion:

The simplified expression $8x^3\cdot \left(2x^2\right)=16\cdot x^5$ , so the exponent of the product is 5.