Question

Express $ {q^{ - 4}} $ as a positive exponent.

Answer 1

Hint: An exponent can be positive or negative. A positive exponent represents the number of times the base is multiplied by itself. For example, $ {5^2} $ is equal to $ 5 \times 5 = 25 $ . A negative exponent represents the number of times the base is divided. For example, $ {5^{ - 2}} $ , then it is written as $ \dfrac{1}{{{5^2}}} $ which is equal to $ \dfrac{1}{{25}} $ .

Complete step by step solution:
In the problem, we have given a negative exponent i.e, $ {q^{ - 4}} $ and we have to convert it into positive exponent and to convert it, here we will use the negative exponent rule, which says that the numerator of negative exponents get moved to the denominator and the sign of the exponent gets changed. Now, on applying this negative exponent rule, we get,
 $ \Rightarrow {q^{ - 4}} = \dfrac{1}{{{q^4}}} $
Hence, the positive exponent is $ \dfrac{1}{{{q^4}}} $ .
So, the correct answer is “ $ \dfrac{1}{{{q^4}}} $ ”.

Note: An exponent is a number which represents the number of times, a number is multiplied by itself. If a is a number whose exponent is b then it is written as $ {a^b} $ which means the number ‘a’ is multiplied by itself, ‘b’ times and it is pronounced as ‘a’ raised to the power of ‘b’. For example, $ {2^3} $ is $ 2 \times 2 \times 2 $ which is equal to $ 8 $ , here $ 2 $ is the base and $ 3 $ is the exponent.
If there is no exponent given to the base then by default, we will take $ 1 $ as its exponent and the result of the number is the number itself, as it means that the number is multiplied by itself only one time. For example, ‘ $ a $ ’, it is also written as $ {a^1} $ which is equal to ‘ $ a $ ’