Solve for the Exponent: (7/4)ˣ = 1

Q: Why does any number to the zero power equal 1?

This comes from the exponent division rule. When you divide powers with the same base: $ \frac{a^n}{a^n} = a^{n-n} = a^0 $. Since any number divided by itself equals 1, we have $ a^0 = 1 $!

Q: Does this rule work for fractions too?

Yes! The zero exponent rule applies to any non-zero number, including fractions, decimals, and negative numbers. So $ (\frac{7}{4})^0 = 1 $, $ (0.5)^0 = 1 $, and $ (-3)^0 = 1 $.

Q: What about 0 to the zero power?

That's a special case! $ 0^0 $ is actually undefined in most contexts because it creates a mathematical contradiction. The zero exponent rule only applies to non-zero bases.

Q: How can I remember this rule?

Think of it as "anything to the zero = hero" (sounds like zero)! Or remember: when you see an equation like $ a^x = 1 $, your first thought should be "x must be 0".

Q: Are there other ways to solve this type of problem?

You could use logarithms: take log of both sides to get $ x \log(\frac{7}{4}) = \log(1) = 0 $, so x = 0. But recognizing the zero exponent rule is much faster!

Zero Exponent Rule with Fraction Bases

$(\frac{7}{4})^?=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's identifying the missing exponent together!

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

00:15 This rule stands as long as the number isn't zero.

00:20 Now, let's apply this concept to our problem and solve it step by step.

00:32 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(\frac{7}{4})^?=1$

Step-by-step solution

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

$X^0=1$ It is thus clear that:

$(\frac{7}{4})^0=1$ Therefore, the correct answer is option C.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Exponent Rule: Any non-zero number raised to power 0 equals 1
Recognition: When $a^x = 1$ , then x = 0 for any a ≠ 0
Verification: Check that $(\frac{7}{4})^0 = 1$ using calculator ✓

Common Mistakes

Avoid these frequent errors

Taking the reciprocal of the base as the exponent
Don't think $(\frac{7}{4})^x = 1$ means x = $\frac{4}{7}$ = wrong answer! This confuses reciprocals with exponents. Always remember the zero exponent rule: any non-zero number to the power 0 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?

This comes from the exponent division rule. When you divide powers with the same base: $\frac{a^n}{a^n} = a^{n-n} = a^0$ . Since any number divided by itself equals 1, we have $a^0 = 1$ !

Does this rule work for fractions too?

Yes! The zero exponent rule applies to any non-zero number, including fractions, decimals, and negative numbers. So $(\frac{7}{4})^0 = 1$ , $(0.5)^0 = 1$ , and $(-3)^0 = 1$ .

What about 0 to the zero power?

That's a special case! $0^0$ is actually undefined in most contexts because it creates a mathematical contradiction. The zero exponent rule only applies to non-zero bases.

How can I remember this rule?

Think of it as "anything to the zero = hero" (sounds like zero)! Or remember: when you see an equation like $a^x = 1$ , your first thought should be "x must be 0".

Are there other ways to solve this type of problem?

You could use logarithms: take log of both sides to get $x \log(\frac{7}{4}) = \log(1) = 0$ , so x = 0. But recognizing the zero exponent rule is much faster!

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