Question

10. Solve this question step by step
Please give verified answer​

Answer 1

Answer:

8

Step-by-step explanation

$\frac{1}{9^3}$ x $\frac{2}{1/6^2}$ x $(\frac{1^1/3}{27^1/3})^-4$                    (16^1/4 = 2 As 2x2x2x2   27^1/3=3)

$\frac{1}{729}$ x 2x36 x $(\frac{1}{3})^-4$

$\frac{1}{729}$ x 2 x 36 x $3^4$

$\frac{1}{729}$ x 2 x 36 x 81

2 x 36/9

8

Answer 2

Answer:

8

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:

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

Therefore, the required answer is 8.

${\underline{{\text{ Some Important Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a}\\\\ a^0 = 1$

[Where all variables are real and greater than 0]

It's Easy, Isn't ?