Question

(4/9)^4/(16/27)^2=? What is the answer for this equation using the laws of indices?

Answer 1

Step-by-step explanation:

$\frac{ {( \frac{4}{9} )}^{4} }{ {( \frac{16}{27}) }^{2} } \\ = \frac{ \frac{ {4}^{4} }{ {9}^{4} } }{ \frac{ {16}^{2} }{ {27}^{2} } } \\ = \frac{ {4}^{4} \times {9}^{ - 4} }{ {16}^{2} \times {27}^{ - 2} } \\ = \frac{ { ({2}^{2} )}^{4} \times { ({3}^{2}) }^{ - 4} }{ {( {2}^{4}) }^{2} \times {( {3}^{3}) }^{ - 4} } \\ = \frac{ {2}^{8} \times {3}^{ - 8} }{ {2}^{8} \times {3}^{ - 12} } \\ = {2}^{8} \times {2}^{ - 8} \times {3}^{ - 8} \times {3}^{12} \\ = {2}^{8 - 8} \times {3}^{ - 8 + 12} \\ = {2}^{0} \times {3}^{4} \\ = 1 \times {3}^{4} \\ = 1 \times 81 \\ = {3}^{4} = 81$

hope you get your answer