Question

What is the power of \[4\] equals \[81\] ?

Answer 1

Hint: In this question it is told to us that we need to find which number when we raise it to the power of \[4\] gives us \[81\] . Here we will use the properties of exponents and factorization to find the factors of \[81\] and then which of those factors when to the power of \[4\] gives us \[81\] .

Complete step by step answer:
 To solve this we will start with taking the prime factors of the number \[81\] . Now according to the question we need to write \[81\] such that we find the number which when raised to four gives us \[81\] . Now firstly we will start this by taking the prime factors of \[81\] which are
\[81=3\times 3\times 3\times 3\]
Now everytime \[3\] is repeated we can write is as a power raised that’s why it will get that;
\[81={{3}^{4}}\]
Now from this we can say that when we raise \[3\] to the power of \[4\] we get \[81\] .
Hence \[3\] to the power of \[4\] equals \[81\] .

Note: Powers and Exponents we can say are used to represent any number in a simplified manner which can make our calculations very easier for us to do. To explain power is a number which shows repeated multiplication of the same number which we can say is a factor. Exponent’s value is based upon the number of times a base is multiplied to itself to give us the value which it is supposed to represent. As we can see here in this question we can see that \[4\] is the exponent here. \[3\] is the base and \[81\] is the number it is supposed to represent.