Question

approximate the following number using a calculator.
$6^{-1.3}$

$6^{-1.3} \approx \boxed{0.027}$ (round to three decimal places as needed.)

Explanation:

Step1: Rewrite negative exponent

$6^{-1.3} = \frac{1}{6^{1.3}}$

Step2: Calculate $6^{1.3}$

First, $6^{1.3}=6^{1+0.3}=6\times6^{0.3}$. Using a calculator, $6^{0.3}\approx1.7623$, so $6\times1.7623\approx10.5738$

Step3: Compute reciprocal

$\frac{1}{10.5738}\approx0.0946$

Step4: Round to 3 decimals

Round 0.0946 to three decimal places: look at the 4th decimal digit (6), which is ≥5, so round up the 3rd decimal digit.

Answer:

$6^{-1.3} \approx 0.095$