Question

1) 7^-22) 2^9:2^143) (5)^-34) (3^-2)^2​

Answer 1

$\boxed {\ a^{-n}=\dfrac{1}{a^{n}}\ }\\\\\\7^{-2}=\dfrac{1}{7^2}=\dfrac{1}{49}\\\\\\2^9:2^{14}=\dfrac{2^9}{2^{14}}=\dfrac{1}{2^5}=\dfrac{1}{32}=0,03125\\\\\\5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}=0,008\\\\\\(3^{-2})^2=3^{-4}=\dfrac{1}{3^4}=\dfrac{1}{81}$

Answer 2

Let's simplify each of the expressions:

1. 7^-2:

   7^-2 = 1 / 7^2 = 1 / 49

2. 2^9 ÷ 2^14:

   When you divide two numbers with the same base (in this case, 2), you can subtract the exponents:

   2^9 ÷ 2^14 = 2^(9 - 14) = 2^(-5)

3. (5)^-3:

   This means to take the reciprocal of 5 cubed:

   (5)^-3 = 1 / 5^3 = 1 / 125

4. (3^-2)^2:

   First, calculate the value inside the parentheses:

   3^-2 = 1 / 3^2 = 1 / 9

   Then, square the result:

   (1 / 9)^2 = 1 / (9^2) = 1 / 81

So, the simplified expressions are:

1. 7^-2 = 1/49
2. 2^9 ÷ 2^14 = 2^(-5)
3. (5)^-3 = 1/125
4. (3^-2)^2 = 1/81