Question - Solving a Negative Fractional Exponent Expression
Solution:
The expression in the image is $$(\frac{8}{27})^{-2/3}$$.To solve this, we can apply the rule for negative exponents and fractional exponents. A negative exponent means that you take the reciprocal of the base, and a fractional exponent means you take the root of the base (the denominator of the fraction) and then raise it to the power of the numerator.Here's the step-by-step calculation:$$\left(\frac{8}{27}\right)^{-2/3} = \left(\frac{27}{8}\right)^{2/3}$$Now we take the cube root of both the numerator and the denominator and then square them because the exponent is $$2/3$$:$$\left(\sqrt[3]{\frac{27}{8}}\right)^2 = \left(\frac{\sqrt[3]{27}}{\sqrt[3]{8}}\right)^2 = \left(\frac{3}{2}\right)^2$$Finally, we square the result:$$\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2} = \frac{9}{4}$$Therefore, $$(\frac{8}{27})^{-2/3}$$ equals $$\frac{9}{4}$$ or 2.25.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com