Question

What is 4 to the 5th power?

Answer 1

Hint: To find the value of 4 to the 5th power, we have to represent it as ${{4}^{5}}$ . We know that when a number, say x, is raised to value, say a, we have to multiply the number, x the number as many times has the power, that is a times. So, we have to multiply 4 five times.

Complete step by step solution:
We have to find the value of 4 to the 5th power. We can represent 4 to the 5th power as ${{4}^{5}}$ . We know that when a number, say x, is raised to value, say a, we have to multiply the number, x the number as many times as the power, that is a times.
${{x}^{a}}=\underbrace{x\times x\times x\times ...x}_{a\text{ times}}$
Hence, we can write ${{4}^{5}}$ as
${{4}^{5}}=4\times 4\times 4\times 4\times 4$
Let us simplify this. We will first multiply the pairs of 4.
$\begin{align}
  & {{4}^{5}}=\left( 4\times 4 \right)\times \left( 4\times 4 \right)\times 4 \\
 & \Rightarrow {{4}^{5}}=16\times 16\times 4 \\
\end{align}$
Now, let us multiply the pair of 16.
$\begin{align}
  & \Rightarrow {{4}^{5}}=\left( 16\times 16 \right)\times 4 \\
 & \Rightarrow {{4}^{5}}=256\times 4 \\
\end{align}$
Now, we have to multiply 256 with 4.
$\Rightarrow {{4}^{5}}=1024$
Hence, the value of 4 to the 5th power is 1024.

Note: Students must know the meaning of ‘raised to’ and ‘to the power of’ to solve these problems. These terms are used to represent the exponents. Let us consider ${{x}^{a}}$ . Here, x is the base and a is the exponent. An exponent refers to the number of times a number, that is, base is multiplied by itself. These are many rules related to exponents.