Question

Find the value :
i) ${\left(\frac{4}{5}\right)}^3÷{\left(\frac{4}{5}\right)}^2$
ii) $4^7÷4^5$

• A. i) $\left(\frac{4}{5}\right)$ii) $4$
  
• B. i) $\left(\frac{4}{5}\right)$
  ii) $49$
  
• C. i) $\left(\frac{4}{5}\right)$
  ii) $7$
  
• D. i) $\left(\frac{4}{5}\right)$ ii) $16$
  

Answer 1

The correct option is D i) $\left(\frac{4}{5}\right)$

ii) $16$

(1)

${\left(\frac{4}{5}\right)}^3÷{\left(\frac{4}{5}\right)}^2$

$={\left(\frac{4}{5}\right)}^3\times {\left(\frac{5}{4}\right)}^2$

$=\frac{4^3}{5^3}\times \frac{5^2}{4^2}$

$=\frac{4^3}{4^2}\times \frac{5^2}{5^3}$

Now apply law of exponents, $\frac{x^m}{x^n}=x^{m-n}$

So, the expression is

$=4^{3-2}\times 5^{2-3}$

$=4^1\times 5^{-1}$

$=\frac{4}{5}$

(2)

$4^7÷4^5$

$=4^7\times \frac{1}{4^5}$

$=\frac{4^7}{4^5}$

Now apply law of exponents, $\frac{x^m}{x^n}=x^{m-n}$

So, the expression is

$=4^{7-5}$

$=4^2$

$=16$