Question

Change this radical to an algebraic expression with fractional exponents. √y^2 The exponent on y is:

Answer 1

The power rule (or law of indices) related to root is given
$x^{ \frac{1}{2} }= \sqrt[2]{x}$

We have $\sqrt{ y^{2} }$
Rewrite according to the rule we have $y^{ \frac{2}{2} } = y^{1}$

The exponent on y is '1'

Answer 2

√y² to an algebraic expression is y and the exponent on y is 1

Algebraic expression:

Algebraic expression is the combination of terms by the operation such as addition, subtraction etc.

Therefore, the radical √y² can be changed to an algebraic expression as follows:

Using law of indices,

√a = $a^{1/2}$ and $a^{b(c)} =a^{bc}$

Therefore,

√y² = $y^{1/2(2)} = y$

Therefore,

√y² to an algebraic expression is y

The exponent on y is 1

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