https://file.aiquickdraw.com/mathbot/file/17297858654908yg83htr.jpg

Let's solve the problems one by one based on the image:

### **Question 13: Rewrite the expression using the same base.**

The given expression is:

\[
(27)^6 \cdot (27)^4
\]

To simplify this expression, we use the property of exponents that states:

\[
a^m \cdot a^n = a^{m+n}
\]

Here, the base is 27, so:

\[
(27)^6 \cdot (27)^4 = 27^{6+4} = 27^{10}
\]

The simplified expression is:

\[
27^{10}
\]

---

### **Question 14: Simplify.**

The given expression is:

\[
w^4 \cdot (w^2) \cdot (w^2)
\]

We can combine the exponents using the same exponent rule:

\[
a^m \cdot a^n = a^{m+n}
\]

First, multiply the two \(w^2\)'s:

\[
w^2 \cdot w^2 = w^{2+2} = w^4
\]

Now, we have:

\[
w^4 \cdot w^4
\]

Again, applying the exponent rule:

\[
w^4 \cdot w^4 = w^{4+4} = w^8
\]

So the simplified expression is:

\[
w^8
\]

---

Would you like more details or have any questions on these problems?

Here are 5 follow-up questions related to these concepts:

1. How would you simplify \((5^3) \cdot (5^7)\)?
2. Can you rewrite \(a^m / a^n\) using a single exponent?
3. What is the result of \( (x^5)^2 \)?
4. How can you express \(2^{10} \cdot 4^3\) using a common base?
5. If \( (y^2)^4 \cdot (y^3)^2 \), how would you simplify it?

**Tip:** When multiplying powers with the same base, just add the exponents.

Rewrite the expression using the same base. (27)^6 * (27)^4
Simplify w^4(w^2)(w^2)

Learn how to simplify expressions with the same base, such as (27)^6 * (27)^4 and w^4 * (w^2) * (w^2), using the exponent addition rule. Suitable 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