Question

please help me ASAP question is attached above​

Answer 1

Answer:

answer is 13/12

Step-by-step explanation:

multiply the outer -1 with both inner -1 by opening the bracket.

then, 4/3 - 1/4 = 16/12 - 3/12 = 13/ 12

Answer 2

Question

$\sf \{ (\frac{4}{3}) ^{-1}-(\frac{1}{4})^{-1} \}^{-1}$

$\rule{300}{1}$

Answer with Steps

We will have to apply this law of exponent ⇒ $\sf a^{-m}=\frac{1}{a^m}$

$\sf \{ (\frac{4}{3}) ^{-1}-(\frac{1}{4})^{-1} \}^{-1}$

$\sf \{ \frac{3}{4} -4 \}^{-1}$

Now we will have to subtract the rational numbers. The steps to do so is below.

Step 1: Find the LCM of the denominators to make them equal.

$\sf L.C.M \ of \ 1\ and \ 4 \ is => 4$

Step 2: Make the denominators equal.

$\sf \{ \frac{3\times 1 }{4\times 1 } -\frac{4\times 4 }{1\times 4 } \}^{-1}$

$\sf \{ \frac{3}{4 } -\frac{16}{ 4 } \}^{-1}$

$\sf \{ \frac{-13}{4 } \}^{-1}$

Now we have to apply this law of exponent again ⇒ $\sf a^{-m}=\frac{1}{a^m}$

$\sf \{ \frac{-13}{4 } \}^{-1} = \frac{-4}{13}$

∴ $\sf \bf \{ (\frac{4}{3}) ^{-1}-(\frac{1}{4})^{-1} \}^{-1} = \frac{-4}{13}$

$\rule{300}{1}$

Additional Information :)

Exponent is a way to express the numbers that are multiplied by the same several times.

For example => $\sf 2 \times 2 \times 2 \times 2\times 2 = 2^5$

Exponents are also known as "powers".

Laws of exponents  

We have 8 main laws of exponents. They are listed below.

• $\sf a^m \times a^n = a^{m+n}$

• $\sf a^{m}\div a^{n} = a^{m-n}$

• $\sf (a^m)^n = a^{m\times n}$

• $\sf a^m \times b^m = (ab)^m$

• $\sf a^m \div b^m = (\frac{a}{b})^m$

• $\sf a^0 =1$

• $\sf \frac{a^m}{b^m} =( \frac{a}{b})^m$

• $\sf a^{-m} = \frac{1}{a^m}$

$\rule{300}{1}$