Question

Simplify :
i) ${\left[{\left(\frac{15}{12}\right)}^3\right]}^4$
ii) $(3^4{)}^{-2}$

• A. i) ${\left(\frac{15}{12}\right)}^3$ii) $(3{)}^2$
  
• B. i) ${\left(\frac{15}{12}\right)}^4$ii) $(3{)}^{-4}$
  
• C. i) ${\left(\frac{15}{12}\right)}^{12}$ii) $(3{)}^{-8}$
  
• D. i) ${\left(\frac{15}{12}\right)}^7$ii) $(3{)}^{-8}$
  

Answer 1

The correct option is C i) ${\left(\frac{15}{12}\right)}^{12}$

ii) $(3{)}^{-8}$

(1)

The expression is,

${\left[{\left(\frac{15}{12}\right)}^3\right]}^4$

Apply the law of exponents, ${\left[{\left(x\right)}^m\right]}^n={\left(x\right)}^{m\times n}$

So the expression is

$={\left(\frac{15}{12}\right)}^{3\times 4}$

$={\left(\frac{15}{12}\right)}^{12}$

$=\frac{{15}^{12}}{{12}^{12}}$

(2)

The expression is,

${\left(3^4\right)}^{-2}$

Apply the law of exponents, ${\left[{\left(x\right)}^m\right]}^n={\left(x\right)}^{m\times n}$

So the expression is

$={\left(3\right)}^{4(-2)}$

$=3^{-8}$

$=\frac{1}{3^8}$