For this math tutor, the end-of-semester rush is about to end. Tutoring for exam prep, you tend to return to those “messy” problems students would rather avoid….

Radical expressions are among the most difficult topics in high school math. Let’s explore an example:

√(x)⁷(⁵√(x)⁹)

Most people would be uncomfortable about this question. It’s really not that hard, as long as you know the exponent law

^a√x^b=x^(b/a)

where a, if not written, is meant to be 2.

We rewrite the expression as follows:

√(x)⁷(⁵√(x)⁹)=x^(7/2)x^(9/5)

The law for multiplying expressions with the same base is to add the exponents. To add these fractional exponents, we need to get a common denominator as follows:

7/2 + 9/5 = 35/10 + 18/10 = 53/10

Therefore, we have

√(x)⁷(⁵√(x)⁹)=x^(7/2)x^(9/5)=x^(53/10)

To simplify, we reverse the exponent law for mutliplication:

x^(53/10)=x^(50/10)*x^(3/10)=x^5*x^(3/10)

Reversing the radical-to-exponent law, we arrive at

x^5*x^(3/10)=x^5(¹⁰√(x)^3)

The answer might seem surprising. In fact, for many, this process might need still further illumination. In future posts, I’ll revisit some of the ideas used in this one. Cheers:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.