https://file.aiquickdraw.com/mathbot/file/1726121087452skin18lp.jpg

Simplify the expression, and eliminate any negative exponents

The given expression is:

\[
\left(3a^4b^{-2}\right)^3 \left(a^8b^{-1}\right)
\]

Let's simplify this step by step:

### Step 1: Expand the powers
We need to distribute the exponent \(3\) across all terms inside the first set of parentheses:

\[
\left(3a^4b^{-2}\right)^3 = 3^3 \cdot a^{4 \cdot 3} \cdot b^{-2 \cdot 3} = 27a^{12}b^{-6}
\]

So, the expression becomes:

\[
27a^{12}b^{-6} \cdot a^8b^{-1}
\]

### Step 2: Combine like terms
Now, combine the powers of \(a\) and \(b\):

For \(a\):
\[
a^{12} \cdot a^8 = a^{12 + 8} = a^{20}
\]

For \(b\):
\[
b^{-6} \cdot b^{-1} = b^{-6 + (-1)} = b^{-7}
\]

### Step 3: Eliminate negative exponents
To eliminate the negative exponent, rewrite \(b^{-7}\) as \(\frac{1}{b^7}\):

\[
27a^{20}b^{-7} = \frac{27a^{20}}{b^7}
\]

### Final Answer:
\[
\frac{27a^{20}}{b^7}
\]

Let me know if you'd like further details or have any other questions!

---

Here are 5 related questions for practice:
1. How would you simplify \((2x^5y^{-3})^4(x^2y^6)\)?
2. What happens if the exponent outside the parentheses is negative?
3. Can you apply this process to an expression with more variables, such as \((xy^{-2}z^3)^2(x^2z^{-1})\)?
4. How do you handle fractional exponents in expressions like this?
5. How do negative exponents affect the overall fraction?

**Tip:** Always combine like terms by adding their exponents, and remember to convert negative exponents to positive by moving them to the denominator or numerator.

Simplify the expression, and eliminate any negative exponents: (3a^4b^{-2})^3(a^8b^{-1})

Learn how to simplify the expression (3a^4b^{-2})^3(a^8b^{-1}) step by step, including distributing exponents, combining like terms, and eliminating negative exponents. Perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation