Evaluate the Expression: Finding the Value of a⁻⁴

Q: Why does a negative exponent make a fraction?

A negative exponent means "how many times do I divide by this base?" So $ a^{-4} $ means divide by a four times, which equals $ \frac{1}{a^4} $.

Q: Does the negative exponent make the answer negative?

No! The negative sign only affects the position of the base (numerator vs denominator). The actual value depends on whether the base itself is positive or negative.

Q: What if the base was negative, like (-a)?

If you had $ (-a)^{-4} $, it would become $ \frac{1}{(-a)^4} $. Since even powers make positive results, this equals $ \frac{1}{a^4} $.

Q: Can I remember this rule with a simple trick?

Yes! Think "negative exponent = flip and make positive." The base flips to the denominator, and the exponent becomes positive: $ a^{-4} \rightarrow \frac{1}{a^4} $.

Q: Why can't a equal zero in this problem?

If a = 0, then $ \frac{1}{a^4} = \frac{1}{0} $ which is undefined! Division by zero is impossible in mathematics, so we must specify $ a \neq 0 $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the following expression

00:03 According to the laws of exponents, any number (A) raised to the power of (N)

00:06 equals 1 divided by the number (A) raised to the power of (-N)

00:09 Let's apply it to the question

00:11 The number (A) becomes 1 divided by (A)

00:14 and the power (-4) becomes -(-4)

00:17 A negative multiplied by a negative becomes positive, hence the exponent is 4

00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$a^{-4}=\text{?}$

$(a\ne0)$

2

Step-by-step solution

We begin by using the negative exponent rule.

$b^{-n}=\frac{1}{b^n}$ We apply it to the problem:

$a^{-4}=\frac{1}{a^4}$ Therefore, the correct answer is option B.

3

Final Answer

$\frac{1}{a^4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative exponents create reciprocals: $a^{-n} = \frac{1}{a^n}$
Technique: Apply the rule: $a^{-4} = \frac{1}{a^4}$
Check: Verify the base stays positive in denominator and exponent becomes positive ✓

Common Mistakes

Avoid these frequent errors

Making the coefficient negative instead of creating a reciprocal
Don't change $a^{-4}$ to $-4a$ or $-\frac{1}{a^4}$ = completely wrong operation! The negative sign in the exponent means reciprocal, not negative coefficient. Always flip to create $\frac{1}{a^4}$ with positive exponent.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does a negative exponent make a fraction?

+

A negative exponent means "how many times do I divide by this base?" So $a^{-4}$ means divide by a four times, which equals $\frac{1}{a^4}$ .

Does the negative exponent make the answer negative?

+

No! The negative sign only affects the position of the base (numerator vs denominator). The actual value depends on whether the base itself is positive or negative.

What if the base was negative, like (-a)?

+

If you had $(-a)^{-4}$ , it would become $\frac{1}{(-a)^4}$ . Since even powers make positive results, this equals $\frac{1}{a^4}$ .

Can I remember this rule with a simple trick?

+

Yes! Think "negative exponent = flip and make positive." The base flips to the denominator, and the exponent becomes positive: $a^{-4} \rightarrow \frac{1}{a^4}$ .

Why can't a equal zero in this problem?

+

If a = 0, then $\frac{1}{a^4} = \frac{1}{0}$ which is undefined! Division by zero is impossible in mathematics, so we must specify $a \neq 0$ .

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Evaluate the Expression: Finding the Value of a⁻⁴

Negative Exponents with Variable Bases

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does a negative exponent make a fraction?

Does the negative exponent make the answer negative?

What if the base was negative, like (-a)?

Can I remember this rule with a simple trick?

Why can't a equal zero in this problem?

🌟 Unlock Your Math Potential

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