Question

How do you simplify $\dfrac{{4{x^2}}}{{2{x^{\dfrac{1}{2}}}}}$?

Answer 1

Hint: Take the given expression and first of all remove the common multiple from the numerator and the denominator and then we will use the law of the negative exponent rule which states that when the power and exponent moved to the denominator negative power becomes positive that is ${a^{ - n}} = \dfrac{1}{{{a^n}}}$and then simplify the expression for the resultant required value.

Complete step by step solution:
Take the given expression: $\dfrac{{4{x^2}}}{{2{x^{\dfrac{1}{2}}}}}$
Common multiples from the numerator and the denominator cancels each other in the above expression.
$ \Rightarrow \dfrac{{2{x^2}}}{{{x^{\dfrac{1}{2}}}}}$
Now, apply negative quotient law ${a^{ - n}} = \dfrac{1}{{{a^n}}}$in the above expression -
$ \Rightarrow 2{x^{2 - \dfrac{1}{2}}}$
Simplify the above expression –
$ \Rightarrow 2{x^{\dfrac{3}{2}}}$
This is the required solution.

Thus the required answer $ 2{x^{\dfrac{3}{2}}}$.

Note: The power is used to express mathematical equations in the short form; it is an expression that represents the repeated multiplication of the same factor. For example - $2 \times 2 \times 2$ can be expressed as ${2^3}$. Here, the number two is called the base and the exponent represents the number of times the base is used as the factor. Remember the seven basic rules of the exponent or the laws of exponents to solve these types of questions. Make sure to go through the below mentioned rules, it describes how to solve different types of exponents problems and how to add, subtract, multiply and divide the exponents.

- Product of powers rule
- Quotient of powers rule
- Power of a power rule
- Power of a product rule
- Power of a quotient rule
- Zero power rule
- Negative exponent rule