What is the fifth root of 1024?
Understand the Problem
The question is asking for the fifth root of the number 1024, which involves calculating a number that, when raised to the power of five, equals 1024.
Answer
$4$
Answer for screen readers
The fifth root of 1024 is $4$.
Steps to Solve
- Identify the required calculation
To find the fifth root of 1024, we need to express this as an exponent. The fifth root can be written as $1024^{1/5}$.
- Rewrite 1024 as a power of a small number
Let's find what 1024 equals when expressed in terms of base 2. We know that $2^{10} = 1024$.
- Set up the equation
Now, we rewrite the fifth root calculation using the base we found: $$ (2^{10})^{1/5} $$
- Use the power of a power property
We apply the property of exponents that states $(a^m)^n = a^{m \cdot n}$: $$ (2^{10})^{1/5} = 2^{10 \cdot \frac{1}{5}} = 2^2 $$
- Calculate the final value
Now, we calculate $2^2$: $$ 2^2 = 4 $$
The fifth root of 1024 is $4$.
More Information
The fifth root of a number is the value that, when multiplied by itself five times, gives the original number. In this case, $4 \times 4 \times 4 \times 4 \times 4 = 1024$.
Tips
- Confusing the roots: Some might mistakenly think the problem involves the square or cube root instead of the fifth root. It's essential to focus on the correct exponent.
- Incorrect calculations with powers: When manipulating exponents, ensure each step uses the correct exponent rules to avoid mistakes.