10. Solve this question step by stepPlease give verified answer. Created by ritika16181. Math

10. Solve this question step by stepPlease give verified answer...

atul9855

Answer:

Step-by-step explanation:

To Simplify:

${9}^{ - 3} \times \dfrac{ {(16)}^{ \frac{1}{4} } }{ {(6)}^{ - 2} } \times {( \dfrac{1}{27} )}^{ - \frac{4}{3} }$

What and how to do ?

This question is related to Laws of Indices.

1.Break the exponent in smallest form.

e.g 27 = 3³, 16 = 2⁴

2.Siplit the factors of exponents as well as powers.

e.g 6² = (3×2)² = 3² × 2²

3. Follow the Laws of Indices and just simplify.

Solution:

${9}^{ - 3} \times \dfrac{ {(16)}^{ \frac{1}{4} } }{ {(6)}^{ - 2} } \times {( \dfrac{1}{27} )}^{ - \frac{4}{3} } \\ \\ = {(3)}^{2.( - 3)} \times \sqrt[4]{16} \times {(6)}^{2} \times {(27)}^{ \frac{4}{3} } \\ \\ = {3}^{ - 6} \times 2 \times {(3 \times 2)}^{2} \times \sqrt[3]{{(27)}^{4}} \\ \\ = {3}^{ - 6} \times 2 \times {3}^{2} \times {2}^{2} \times {3}^{4} \\ \\ = {3}^{( - 6 + 2 + 4)} \times 2 \times 4 \\ \\ = {3}^{0} \times 8 \\ \\ = 8$