Solve (300 × 5/3 × 2/7)⁰: Understanding the Zero Power Rule

Q: Do I really need to calculate what's inside the parentheses?

No! The zero power rule says any non-zero number to the power of 0 equals 1. Since $ 300 \cdot \frac{5}{3} \cdot \frac{2}{7} $ is clearly not zero, the answer is immediately 1.

Q: What if the expression inside equals zero?

If the base were zero, then $ 0^0 $ would be undefined in most contexts. But here, $ 300 \cdot \frac{5}{3} \cdot \frac{2}{7} = \frac{1000}{7} $ which is definitely not zero!

Q: Why is anything to the power of 0 equal to 1?

Think of it this way: $ x^3 ÷ x^3 = x^{3-3} = x^0 $. But $ x^3 ÷ x^3 = 1 $ (any number divided by itself equals 1). So $ x^0 = 1 $!

Q: Does this work for negative numbers too?

Yes! $ (-5)^0 = 1 $, $ (-\frac{3}{4})^0 = 1 $. The zero power rule works for any non-zero number, positive or negative.

Q: What about fractions raised to the power of 0?

Same rule applies! $ (\frac{7}{8})^0 = 1 $, $ (\frac{1000}{7})^0 = 1 $. As long as the fraction isn't $ \frac{0}{n} = 0 $, the answer is always 1.

Zero Power Rule with Complex Expressions

$(300\cdot\frac{5}{3}\cdot\frac{2}{7})^0=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem together.

00:11 Remember, any number raised to the power of zero equals one.

00:16 This is true as long as the number itself is not zero.

00:20 Now, let's use this rule to solve our exercise.

00:26 And there you have it. That's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(300\cdot\frac{5}{3}\cdot\frac{2}{7})^0=\text{?}$

Step-by-step solution

Due to the fact that raising any number (except zero) to the power of zero will give the result 1:

$X^0=1$ Let's examine the expression of the problem:

$(300\cdot\frac{5}{3}\cdot\frac{2}{7})^0$ The expression inside of the parentheses is clearly not 0 (it can be calculated numerically and verified)

Therefore, the result of raising to the power of zero will give the result 1, that is:

$(300\cdot\frac{5}{3}\cdot\frac{2}{7})^0 =1$ Therefore, the correct answer is option A.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Power Rule: Any non-zero expression raised to power 0 equals 1
Technique: Don't calculate the base - if $x \neq 0$ , then $x^0 = 1$
Check: Verify the base is non-zero: $300 \cdot \frac{5}{3} \cdot \frac{2}{7} = \frac{1000}{7} \neq 0$ ✓

Common Mistakes

Avoid these frequent errors

Calculating the complex expression inside parentheses first
Don't waste time computing $300 \cdot \frac{5}{3} \cdot \frac{2}{7} = \frac{1000}{7}$ then raising to power 0 = unnecessary work! The zero power rule applies immediately to any non-zero base. Always recognize that if the base isn't zero, the answer is instantly 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

Do I really need to calculate what's inside the parentheses?

No! The zero power rule says any non-zero number to the power of 0 equals 1. Since $300 \cdot \frac{5}{3} \cdot \frac{2}{7}$ is clearly not zero, the answer is immediately 1.

What if the expression inside equals zero?

If the base were zero, then $0^0$ would be undefined in most contexts. But here, $300 \cdot \frac{5}{3} \cdot \frac{2}{7} = \frac{1000}{7}$ which is definitely not zero!

Why is anything to the power of 0 equal to 1?

Think of it this way: $x^3 ÷ x^3 = x^{3-3} = x^0$ . But $x^3 ÷ x^3 = 1$ (any number divided by itself equals 1). So $x^0 = 1$ !

Does this work for negative numbers too?

Yes! $(-5)^0 = 1$ , $(-\frac{3}{4})^0 = 1$ . The zero power rule works for any non-zero number, positive or negative.

What about fractions raised to the power of 0?

Same rule applies! $(\frac{7}{8})^0 = 1$ , $(\frac{1000}{7})^0 = 1$ . As long as the fraction isn't $\frac{0}{n} = 0$ , the answer is always 1.

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