Solve (9×7×8)^(-8): Negative Exponent Expression

Q: Why does a negative exponent create a fraction?

A negative exponent tells you to take the reciprocal! Think of it as: "flip it and make the exponent positive." So $ x^{-3} $ becomes $ \frac{1}{x^3} $.

Q: Does the negative exponent affect what's inside the parentheses?

No! The base $ (9×7×8) $ stays exactly the same. Only the exponent changes from -8 to +8 when you take the reciprocal.

Q: Is this the same as a negative number?

Absolutely not! $ (9×7×8)^{-8} $ gives a positive fraction, not a negative number. The negative is in the exponent position, not making the answer negative.

Q: Do I need to calculate 9×7×8 first?

Not necessarily! You can leave it as $ \frac{1}{(9×7×8)^8} $ since the question asks for the equivalent expression, not the final numerical answer.

Q: What if I see a double negative like a^(-(-5))?

Two negatives make a positive! So $ a^{-(-5)} = a^5 $. The negative exponent rule only applies when the final exponent is negative.

Negative Exponents with Product Bases

Choose the expression that corresponds to the following:

$\left(9\times7\times8\right)^{-8}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's simplify this problem together.

00:12 Remember! When we have a negative exponent...

00:16 We use the reciprocal to make the exponent positive.

00:20 Let's apply this to our example.

00:22 First, write the reciprocal as one divided by the number.

00:27 Then, raise it to the positive exponent.

00:30 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the expression that corresponds to the following:

$\left(9\times7\times8\right)^{-8}=$

Step-by-step solution

To solve the expression $\left(9\times7\times8\right)^{-8}$ , we need to apply the power of a product rule combined with the rule for negative exponents. The rule states that $a^{-n} = \frac{1}{a^n}$ . So, a negative exponent indicates a reciprocal.

According to the power of a product rule, if you have a product raised to a power, it is the same as each factor being raised to that power: $(a \times b)^n = a^n \times b^n$ .

So, applying the negative exponent rule to the original expression:

Given: $\left(9\times7\times8\right)^{-8}$ .
Convert the negative exponent to positive by taking the reciprocal: $\frac{1}{\left(9\times7\times8\right)^8}$ .

The correct expression after applying these rules is:

$\frac{1}{(9\times7\times8)^8}$ .

Final Answer

$\frac{1}{\left(9\times7\times8\right)^8}$

Key Points to Remember

Essential concepts to master this topic

Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$ converts negative to positive
Technique: Keep the base unchanged: $(9×7×8)^{-8} = \frac{1}{(9×7×8)^8}$
Check: Negative exponent means reciprocal, not negative number ✓

Common Mistakes

Avoid these frequent errors

Making the result negative instead of taking reciprocal
Don't write $(9×7×8)^{-8} = -(9×7×8)^8$ = negative number! The negative exponent creates a reciprocal, not a negative sign. Always remember: negative exponent means 1 divided by the 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 create a fraction?

A negative exponent tells you to take the reciprocal! Think of it as: "flip it and make the exponent positive." So $x^{-3}$ becomes $\frac{1}{x^3}$ .

Does the negative exponent affect what's inside the parentheses?

No! The base $(9×7×8)$ stays exactly the same. Only the exponent changes from -8 to +8 when you take the reciprocal.

Is this the same as a negative number?

Absolutely not! $(9×7×8)^{-8}$ gives a positive fraction, not a negative number. The negative is in the exponent position, not making the answer negative.

Do I need to calculate 9×7×8 first?

Not necessarily! You can leave it as $\frac{1}{(9×7×8)^8}$ since the question asks for the equivalent expression, not the final numerical answer.

What if I see a double negative like a^(-(-5))?

Two negatives make a positive! So $a^{-(-5)} = a^5$ . The negative exponent rule only applies when the final exponent is negative.

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