Chapter 9, Problem 9PT

To determine

To calculate:To find product or quotient and express using exponents for the below expression:

  $9^2\cdot 9^6$

Answer to Problem 9PT

The product of the expression $9^2\cdot 9^6$ is $9^8$ .

Explanation of Solution

Given information:

Given expression is $9^2\cdot 9^6$

Formula Used:

Product rule of the exponent states that “when multiplying two powers that have the same base, exponents can be added”:

  $a^m\times a^n=a^{m+n}$

Calculation:

Given expression is $9^2\cdot 9^6$

Using the above explanation for the Product rule of the exponent, we have:

  $9^2\cdot 9^6=9^{2+6}$

Solving the above equation, we have:

  $9^2\cdot 9^6=9^8$

Thus, the product of the expression $9^2\cdot 9^6$ is $9^8$ .

Conclusion:

The product of the expression $9^2\cdot 9^6$ is $9^8$ .