Question

1. write a simplified expression using exponents. (5x^5)(2x^7)=(25x)(14x)

Explanation:

Step1: Multiply coefficients

Multiply 5 and 2, so $5\times2 = 10$.

Step2: Use exponent - product rule

For the variables with the same base $x$, when multiplying $x^m$ and $x^n$, we have $x^m\times x^n=x^{m + n}$. Here $m = 5$ and $n=7$, so $x^5\times x^7=x^{5 + 7}=x^{12}$.

Step3: Combine results

The product of $(5x^5)(2x^7)$ is $10x^{12}$.

Answer:

$10x^{12}$