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

  1. 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 $1024^{1/5}$.

  1. 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 $2^{10} = 1024$.

  1. Set up the equation

Now, we rewrite the fifth root calculation using the base we found: $$ (2^{10})^{1/5} $$

  1. Use the power of a power property

We apply the property of exponents that states $(a^m)^n = a^{m \cdot n}$: $$ (2^{10})^{1/5} = 2^{10 \cdot \frac{1}{5}} = 2^2 $$

  1. 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.

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