Solve (1/5)^0: Applying the Zero Exponent Rule

Q: Does this work for fractions too?

Yes! The zero exponent rule works for any non-zero number, including fractions. So $ (\frac{1}{5})^0 = 1 $, $ (\frac{7}{3})^0 = 1 $, and even $ (-\frac{2}{9})^0 = 1 $.

Q: What if the base was 0?

Great question! $ 0^0 $ is actually undefined in mathematics. The zero exponent rule only applies to non-zero bases. Since $ \frac{1}{5} ≠ 0 $, we can safely use the rule here.

Q: How is this different from 0 × anything = 0?

Don't confuse multiplication by zero with exponents of zero! When you multiply by zero, you get zero. But when you raise a non-zero number to the zero power, you get 1. These are completely different operations.

Q: Will I always get 1 when I see exponent 0?

As long as the base is not zero, yes! Whether it's $ 2^0 $, $ 100^0 $, or $ (\frac{1}{5})^0 $, the answer is always 1. This makes zero exponent problems quick to solve!

Zero Exponent Rule with Fractional Bases

$(\frac{1}{5})^0=$

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Step-by-step video solution

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00:00 Solve

00:03 Any number (M) raised to the power of 0 is always equal to 1

00:07 We will use this formula in our exercise

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(\frac{1}{5})^0=$

Step-by-step solution

To solve this problem, let's analyze the expression $(\frac{1}{5})^0$ .

Step 1: Identify the base and exponent
The base is $\frac{1}{5}$ , and the exponent is $0$ .
Step 2: Apply the zero exponent rule
The zero exponent rule states that any non-zero number raised to the power of zero is $1$ . This rule applies universally to all real numbers except zero.
Conclusion
Using the rule, $(\frac{1}{5})^0 = 1$ .

Therefore, the value of the expression $(\frac{1}{5})^0$ is $1$ . Thus, the correct answer is choice $2$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Any non-zero number raised to the zero power equals one
Technique: Identify base $\frac{1}{5}$ is non-zero, so $(\frac{1}{5})^0 = 1$
Check: Apply rule directly: any base ≠ 0 with exponent 0 gives 1 ✓

Common Mistakes

Avoid these frequent errors

Thinking the answer is zero because the exponent is zero
Don't assume $(\frac{1}{5})^0 = 0$ just because the exponent is zero = completely wrong answer! The exponent tells you what to do to the base, not what the result becomes. Always remember: any non-zero base to the zero power equals 1.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to $$ 100^0 $$ ?

FAQ

Everything you need to know about this question

Why does any number to the zero power equal 1?

Think of it this way: when you divide powers with the same base, you subtract exponents. For example, $\frac{5^3}{5^3} = 5^{3-3} = 5^0$ . But $\frac{5^3}{5^3} = \frac{125}{125} = 1$ . So $5^0 = 1$ !

Does this work for fractions too?

Yes! The zero exponent rule works for any non-zero number, including fractions. So $(\frac{1}{5})^0 = 1$ , $(\frac{7}{3})^0 = 1$ , and even $(-\frac{2}{9})^0 = 1$ .

What if the base was 0?

Great question! $0^0$ is actually undefined in mathematics. The zero exponent rule only applies to non-zero bases. Since $\frac{1}{5} ≠ 0$ , we can safely use the rule here.

How is this different from 0 × anything = 0?

Don't confuse multiplication by zero with exponents of zero! When you multiply by zero, you get zero. But when you raise a non-zero number to the zero power, you get 1. These are completely different operations.

Will I always get 1 when I see exponent 0?

As long as the base is not zero, yes! Whether it's $2^0$ , $100^0$ , or $(\frac{1}{5})^0$ , the answer is always 1. This makes zero exponent problems quick to solve!

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