Unravel the Mystery: What is |5^0|?

Q: Does the absolute value change anything here?

Not in this case! Since $ 5^0 = 1 $ and 1 is already positive, the absolute value doesn't change it. So $ |5^0| = |1| = 1 $.

Q: What if the base was negative, like (-3)^0?

Even negative bases follow the zero exponent rule! $ (-3)^0 = 1 $, so $ |(-3)^0| = |1| = 1 $. The zero exponent always gives 1 for any non-zero base.

Q: Is there ever a time when something to the power of 0 doesn't equal 1?

Yes! The special case is $ 0^0 $, which is undefined in most contexts. But for any non-zero number raised to the power of 0, the answer is always 1.

Q: How do I remember this rule?

Try this memory trick: "Zero power = ONE answer". Or remember that when you divide identical numbers (like $ \frac{7^5}{7^5} $), you always get 1, and that's the same as the base to the zero power!

Zero Exponents with Absolute Value

$\left|5^0\right|=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|5^0\right|=$

Step-by-step solution

The expression inside the absolute value is $5^0$ . According to the rules of exponents, any non-zero number raised to the power of 0 is 1. Thus, $5^0 = 1$ .

Next, we apply the absolute value to this result. The absolute value of a number is its distance from zero on a number line, without considering direction, meaning it's always non-negative.

Therefore, $\left|1\right| = 1$ . So, the final answer is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Zero Exponent Rule: Any non-zero number to power 0 equals 1
Technique: Calculate $5^0 = 1$ first, then apply absolute value
Check: Verify $|1| = 1$ since 1 is already positive ✓

Common Mistakes

Avoid these frequent errors

Confusing zero exponent with zero result
Don't think $5^0 = 0$ just because the exponent is zero = wrong answer of 0! The zero exponent rule states any non-zero base raised to power 0 equals 1, not 0. Always remember: $a^0 = 1$ when a ≠ 0.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

Why does any number to the power of 0 equal 1?

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

Does the absolute value change anything here?

Not in this case! Since $5^0 = 1$ and 1 is already positive, the absolute value doesn't change it. So $|5^0| = |1| = 1$ .

What if the base was negative, like (-3)^0?

Even negative bases follow the zero exponent rule! $(-3)^0 = 1$ , so $|(-3)^0| = |1| = 1$ . The zero exponent always gives 1 for any non-zero base.

Is there ever a time when something to the power of 0 doesn't equal 1?

Yes! The special case is $0^0$ , which is undefined in most contexts. But for any non-zero number raised to the power of 0, the answer is always 1.

How do I remember this rule?

Try this memory trick: "Zero power = ONE answer". Or remember that when you divide identical numbers (like $\frac{7^5}{7^5}$ ), you always get 1, and that's the same as the base to the zero power!

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