# Grade 9 Math: Linear Relations and Equations Rational Exponents

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True
False

### Simplify the following statement: $$\Bigg(\frac{a^{\frac{1}{2}}\times b^{-\frac{1}{3}}}{a^{-\frac{7}{4}}\times b^{\frac{2}{3}}}\Biggr)^{-\frac{1}{6}}$$

$$\frac{a^{\frac{1}{6}}}{b^{\frac{3}{8}}}$$
$$\frac{b^{\frac{1}{6}}}{a^{\frac{3}{8}}}$$
$$\frac{b^{\frac{2}{4}}}{a^{\frac{1}{3}}}$$
$$\frac{b^{\frac{1}{2}}}{a^{\frac{1}{8}}}$$

### Simplify the following statement: $$\sqrt[3]{x^2}\times \sqrt{x^3}$$

$$x$$
$$x^2$$
$$x^3$$
$$x^4$$

### Simplify the following statement: $$x^{\frac{1}{4}}\times \sqrt[4]{x^3}\times (x^4)^{2}$$

$$x^9$$
$$x^6$$
$$x^3$$
none of the above
### Simplify the following statement: $$\frac{(\sqrt[3]{x^2}\times x^{\frac{25}{6}})}{(\sqrt[4]{x^3}\times (x^2)^{2})}$$
$$\sqrt[x]{12}$$
$$\sqrt[x^{12}]{x}$$
$$\sqrt{x}$$
$$\sqrt{x^{12}}$$