Chapter 9, Problem 14SGR

To determine

To calculate:To write below expression using exponents:

  $f\cdot f\cdot g\cdot g\cdot g\cdot g$

Answer to Problem 14SGR

The exponent form of the expression $f\cdot f\cdot g\cdot g\cdot g\cdot g$ is $f^2\cdot g^4$ .

Explanation of Solution

Given information:

Given expression is $f\cdot f\cdot g\cdot g\cdot g\cdot g$

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 $f\cdot f\cdot g\cdot g\cdot g\cdot g$

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

  $f\cdot f\cdot g\cdot g\cdot g\cdot g=f^{1+1}\cdot g^{1+1+1+1}$

Solving the above equation, we have:

  $f\cdot f\cdot g\cdot g\cdot g\cdot g=f^2\cdot g^4$

Thus, the exponent formof the expression $f\cdot f\cdot g\cdot g\cdot g\cdot g$ is $f^2\cdot g^4$ .

Conclusion:

The exponent form of the expression $f\cdot f\cdot g\cdot g\cdot g\cdot g$ is $f^2\cdot g^4$ .