2-20-24 Radicals and Rational Exponents Notes

P4. Match the following Properties of Exponents.

P4. Match the following Properties of Exponents.

P5 1A-D. I would use the ​ (a)   Property to simply $$\left(3^{\frac{1}{2}}\right)^2$$ to ​ (b)   which shows that $$3^{\frac{1}{2}}$$ =​ (c)   . Generalized that would be $$a^{\frac{1}{2}}$$ =​ (d)   .​

Radicals and Rational Exponents are inverses of each other and can be inverted as follows $$a^{\frac{m}{n}}=\sqrt[n]{a^m}$$ . Match the exponential terms with their radical equivalent.

Why is $$x^{\frac{3}{2}}=x\sqrt[]{x}$$ ? Reorder the steps to simplify the expression.

Why is $$\left(x^4y\right)^{\frac{1}{2}}=x^2\sqrt[]{y}$$ ? Reorder the steps to simplify the expression.

Why is $$18^{\frac{1}{2}}=3\sqrt[]{2}$$ ? Reorder the steps to simplify the expression.

Use the properties of exponents to simplify $$64^{\frac{1}{2}}$$

Use the properties of exponents to simplify $$\left(\frac{1}{16^{-\frac{1}{4}}}\right)^2$$

P7 A-F. Organize these equivalent expressions under the property that justifies them.