Question

Express square root 125 using rational exponents in two different ways,one with base and the other with base 25.

Use the properties of exponents to show that the two expressions you wrote above are equivalent to square root 125.

Answer 1

Exponents can be written in exponential or radical form.
Exponential form: 125∧ 1/2 means square root of 125.
125∧ 1/2 is 25 because:
25² means+> 25 × 25 = 125

radical form:√125 is 25
25² = 125
let us say x is the base.
x² = x.x
25² = 25 × 25
= 125
To the power of 2 means the base will be multiplied twice.