Question

What is $\dfrac{3}{2}$ to the fourth power?

Answer 1

Hint: Exponents are shorthand for repeated multiplication of the same thing by itself. For example, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in $5\times 5\times 5={{5}^{3}}$ . The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, which being 5 in this example, is called the "base".

Complete step-by-step answer:
This process of using exponents is called raising to a power, where the exponent is the power. The expression ${{5}^{3}}$ is pronounced as "five, raised to the third power" or "five to the third".
So, from the question we need to find the fourth power of the fraction $\left( \dfrac{3}{2} \right)$ .
So, for that what we will do is we will raise the complete fraction to the power four such as
${{\left( \dfrac{3}{2} \right)}^{4}}$ .
Now we will distribute this power to both the numerator and denominator and write it as
${{\left( \dfrac{3}{2} \right)}^{4}}=\dfrac{{{3}^{4}}}{{{2}^{4}}}$
Now in order to evaluate this given value firstly we will have to multiply three by three four times and then multiply two by two four times and then substitute those values in the place of numerator and denominator which are raised to the power four as mentioned in the question and what we will get is:
$\dfrac{81}{16}$ .

Note: Remember to distribute the powers correctly and cancel out the terms if they are same in numerator and denominator. Power must be carefully cancelled and also simplified carefully as there are chances of error.