Exercise 17 Page 364

We are given a numeric expression, and want to write an equivalent expression. m^8/m^6 * m^(10) * m^2/m^9 Notice that this expression involves the product of two powers with the same base. Therefore, we can use the Product of Powers Property. This property states that when multipling two exponential expressions with the same base, we add the exponents.

m^8/m^6 * m^(10) * m^2/m^9

MultPow

a^m*a^n=a^(m+n)

m^8/m^6 * m^(10+2)/m^9

AddTerms

Add terms

m^8/m^6 * m^(12)/m^9

Now, we have the quotient of two powers with the same base. Therefore, we can use the Quotient of Powers Property. This property states that when dividing two exponential expressions with the same base, we subtract the exponents.

m^8/m^6 * m^(12)/m^9

DivPow

a^m/a^n= a^(m-n)

m^(8-6) * m^(12-9)

SubTerm

Subtract term

m^2 * m^3

Finally, let's use again the Product of Powers Property to simplify the expression.

m^2 * m^3

MultPow

a^m*a^n=a^(m+n)

m^(2+3)

AddTerms

Add terms

m^5