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Evaluate
(0.027)^(-(1)/(3))(2pts)

$16$ . Evaluate $(0.027)^{-\frac{1}{3}}(2 \mathrm{pts})$

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Evaluate rational exponents

Full solution

Q.

16

. Evaluate

(0.027)^{-\frac{1}{3}}(2 \mathrm{pts})

Convert to Fraction: First, let's write $0.027$ as a fraction in terms of a power of $3$ . $\newline$ $0.027 = \frac{27}{1000} = \frac{3^3}{10^3}$
Apply Negative Exponent Rule: Now, let's apply the negative exponent rule which is $a^{-n} = \frac{1}{a^n}$ . $\newline$ $(0.027)^{-\frac{1}{3}} = \left( \frac{3^3}{10^3} \right)^{-\frac{1}{3}}$
Use Exponent Property: Next, we'll use the property of exponents that says $(\frac{a}{b})^n = \frac{a^n}{b^n}$ . $\left( \frac{3^3}{10^3} \right)^{-\frac{1}{3}} = \frac{(3^3)^{-\frac{1}{3}}}{(10^3)^{-\frac{1}{3}}}$
Simplify Parts: Now, we simplify each part separately. $\newline$ $(3^3)^{-(1)/(3)} = 3^{3*(-1/3)} = 3^{-1} = \frac{1}{3}$ $\newline$ $(10^3)^{-(1)/(3)} = 10^{3*(-1/3)} = 10^{-1} = \frac{1}{10}$
Divide Results: Finally, we divide the two results. $(\frac{1}{3}) / (\frac{1}{10}) = (\frac{1}{3}) \times (\frac{10}{1}) = \frac{10}{3}$

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