Question

Which of the following statements are true ?

${\left(\frac{5}{10}\right)}^3\times {\left(\frac{3}{10}\right)}^3={\left(\frac{15}{10}\right)}^3$.

• A. True
• B. False

Answer 1

The correct option is B False

Given; ${\left(\frac{5}{10}\right)}^3\times {\left(\frac{3}{10}\right)}^3={\left(\frac{15}{10}\right)}^3$.

We know that

${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{b}}^{\mathrm{m}}={\left(\mathrm{ab}\right)}^{\mathrm{m}}$

Now,

LHS $={\left(\frac{5}{10}\right)}^3\times {\left(\frac{3}{10}\right)}^3$

$$\begin{gathered} ={\left(\frac{5}{10}\times \frac{3}{10}\right)}^3 \\ ={\left(\frac{15}{100}\right)}^3 \end{gathered}$$

≠ RHS

Hence, given statement is false.