Question 74

$$\sqrt[3]{x^6}\times\sqrt[3]{x^{-12}} \times x^{-3} \times \sqrt[3]{x^{9}}$$

Solution

Expression : $$\sqrt[3]{x^6}\times\sqrt[3]{x^{-12}} \times x^{-3} \times \sqrt[3]{x^{9}}$$

We know that, $$\sqrt{x} = x^{\frac{1}{2}}$$

= $$(x)^{\frac{6}{3}} \times (x)^{\frac{-12}{3}} \times \frac{1}{x^3} \times (x)^{\frac{9}{3}}$$

= $$(x)^2 \times (x)^{-4} \times \frac{1}{x^3} \times (x)^3$$

= $$(x)^{2 - 4} \times 1$$

= $$(x)^{-2} = \frac{1}{x^2}$$

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