Susan L. answered • 09/17/13

Tutor

5
(11)
Tutor in Math and Science--Patient, Proficient, Organized

When you say equivalent expression do you mean simplified expression?

If so, for this example I will write it out using ^ to represent the exponent

6 exponent 21 is 6^21 (6 raised to the 21st power which is 6 multiplied by itself 21 times)

Writing the expression you wrote with the ^ is:

6^21 x 10^7/30^7

Using some laws of exponents

a^(mxn) =(a^m)^n

a^m x b^m = (axb)^m

a^m/b^m = (a/b)^m

and factors we can simplify the above.

Express 6^21 as (6^3)^7:

(6^3)^7 x 10^7/30^7

Perform multiplication and division of bases and raise to common power of 7

(6^3 x 10/30)^7

Express all numbers as factors to simplify base (or can multiply and divide)*

((6x6x6) x (2x5)/(6x5))^7

Simplify

((6x6x6) x (2x5)/(6x5))^7 = (6x6x2)^7 = 72^7

*If you multiplied and divided would get (2160/30)^7 = 72^7

Writing the expression you wrote with the ^ is:

6^21 x 10^7/30^7

Using some laws of exponents

a^(mxn) =(a^m)^n

a^m x b^m = (axb)^m

a^m/b^m = (a/b)^m

and factors we can simplify the above.

Express 6^21 as (6^3)^7:

(6^3)^7 x 10^7/30^7

Perform multiplication and division of bases and raise to common power of 7

(6^3 x 10/30)^7

Express all numbers as factors to simplify base (or can multiply and divide)*

((6x6x6) x (2x5)/(6x5))^7

Simplify

((6x6x6) x (2x5)/(6x5))^7 = (6x6x2)^7 = 72^7

*If you multiplied and divided would get (2160/30)^7 = 72^7