Question

Answer these with full solution. irrelevant answer will be reported . ​

Answer 1

11. $((\frac{1}{2} )^{-1} + (\frac{2}{3}) ^{2} - (\frac{3}{4})^{0} )^{-2}$

First, we will apply the zero power rule and the negative exponent inside the bracket.

Zero Power Law ⇒ $a^{0 } = 1$

Negative Power Law ⇒ $a^{-1} = \frac{1}{a}$

$((2)+(\frac{2}{3})^{2} - 1)^{-2}$

Now we will substitute the values and give a whole value to all numbers.

$(2+\frac{4}{9} -1)^{-2}$ =   $(\frac{13}{9})^{-2}$ = $(\frac{9}{13})^{2}$

Now we can find the value of $(\frac{9}{13})^{2}$ which is $\frac{81}{169}$.

12. $(1^{2}+2^{2} + 3^{2})^{\frac{1}{2} }$

First, we will find the value of the numbers in the brackets.

$(1+4+9)^{\frac{1}{2} }$ = $(14)^{\frac{1}{2} }$

$(14)^{\frac{1}{2} } = \sqrt{14}$