QuestionSimplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) $\sqrt{y^{26}}=$ $\square$ (b) $\sqrt{w^{4}}=$ $\square$

Studdy Solution
Recognize that $\sqrt{w^{4}}$ can be rewritten using the property of exponents: $\sqrt{w^{4}} = (w^{4})^{1/2}$.
$$(w^{4})^{1/2} = w^{4 \times \frac{1}{2}} = w^{2}$$
Since the exponent is even, we must consider the absolute value to ensure the result is non-negative:
$$\sqrt{w^{4}} = |w^{2}| = |w|^2$$
The simplified expressions are: (a) $\sqrt{y^{26}} = y^{13}$ (b) $\sqrt{w^{4}} = |w|^2$