Question

Please give answers for the questions below

Answer 1

Answer:

1. $256^{0.16} * 256^{0.09}$ is in the form aᵇ×aⁿ=a⁽ᵇ⁺ⁿ⁾

Thus, $256^{0.16} * 256^{0.09}=256^{0.25}=256^{25/100}=256^{1/4}=\sqrt[4]{256}=4$

option a is correct.

2. $\sqrt[4]{(81)^{-2} }=\sqrt[4]{(9^{2} )^{-2} }=\sqrt[4]{9^{-4}}=1/9$

3.  0.78bar=0.78787878....

Let x=0.78787878.....(1)

Multiply 100 on both sides.

100x=78.787878.....(2)

Subtract (1) and (2). You will get:

99x=78

x=78/99

x=26/33.

4. $\frac{1}{\sqrt{4}-\sqrt{8} }=\frac{1*2+\sqrt{8} }{2-\sqrt{8}*2+\sqrt{8} }=\frac{2+\sqrt{8} }{2^{2}-\sqrt{8}^{2} }=\frac{2+\sqrt{8} }{-4}$

So, either the options are wrong or the question is wrong.

5. x+y=12

Square on Both Sides.

(x+y)²=12²

x²+y²+xy=12

(xy=32)

x²+y²+32=144

x²+y²=112.

6. The expression can be written as:

$\Large \frac{ \left(2.3+0.3\right)\left[ \left(2.3\right)^{2}-0.6+0.09 \right] }{ \left(2.3\right)^{2}-0.69+0.09 }$

$=2.3-0.3$

$=2$

Option a is correct.

7. $\frac{9^{1/3}*27^{-1/2} }{3^{1/6}*3^{-2/3} } =\frac{9^{1/3}*3^{2/3}}{3^{1/6}*27^{1/2}} =\frac{3^{2/3}*3^{2/3}}{3^{1/6}*3^{3/2}}=\frac{3^{4/3}}{3^{5/3}}=3^{4/3-5/3}=3^{-1/3}$

This question took a lot of effort and time, please mark as brainliest!

HOPE THIS HELPS :D