Question

these examples show the application of the negative exponent property. which two examples correctly apply this property?
$17^{\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}$
$6^{-\frac{1}{4}} = -6^{\frac{1}{4}}$
$9^{\frac{1}{4}} = \frac{1}{9^{-\frac{1}{4}}}$
$8^{-\frac{1}{4}} = \frac{1}{8^{\frac{1}{4}}}$
$x^{-\frac{1}{4}} = \frac{x}{x^{\frac{1}{4}}}$

Explanation:

Step1: Recall negative exponent rule

The negative exponent property states $a^{-n} = \frac{1}{a^n}$ for $a
eq 0$.

Step2: Check first example

Verify $17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}$:
Matches $a^{-n} = \frac{1}{a^n}$, so correct.

Step3: Check second example

Verify $6^{-\frac{1}{4}} = -6^{\frac{1}{4}}$:
Negative exponent does not flip sign, so incorrect.

Step4: Check third example

Verify $y^{\frac{1}{4}} = \frac{1}{y^{-\frac{1}{4}}}$:
Rewrite right-hand side: $\frac{1}{y^{-\frac{1}{4}}} = y^{\frac{1}{4}}$, which matches left-hand side, so correct.

Step5: Check fourth example

Verify $8^{-\frac{1}{4}} = -\frac{1}{8^{\frac{1}{4}}}$:
Negative exponent does not add negative sign, so incorrect.

Step6: Check fifth example

Verify $x^{-\frac{2}{4}} = \frac{x^{\frac{2}{4}}}{1}$:
$x^{-\frac{2}{4}} = \frac{1}{x^{\frac{2}{4}}}$, which does not match, so incorrect.

Answer:

• $17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}$
• $y^{\frac{1}{4}} = \frac{1}{y^{-\frac{1}{4}}}$