Question

Exponent properties 4rk^4 x 7r^5k^6 show ur work

Answer 1

To simplify the expression \( 4r k^4 \times 7r^5 k^6 \), we can follow the properties of exponents and multiplication.

Here are the steps we'll take:

1. **Multiply the coefficients** (numerical parts).
2. **Combine like terms** (both for \( r \) and for \( k \)) using the properties of exponents.

Let's break it down step by step.

### Step 1: Multiply the coefficients

The coefficients are \( 4 \) and \( 7 \):
\[
4 \times 7 = 28
\]

### Step 2: Combine the \( r \) terms

We have \( r \) and \( r^5 \). When multiplying terms with the same base, we add the exponents:
\[
r \times r^5 = r^{1+5} = r^6
\]

### Step 3: Combine the \( k \) terms

We have \( k^4 \) and \( k^6 \). Again, we add the exponents:
\[
k^4 \times k^6 = k^{4+6} = k^{10}
\]

### Step 4: Combine all parts

Now we combine the results from the previous steps:
\[
28r^6k^{10}
\]

### Final Result

Thus, the expression \( 4rk^4 \times 7r^5k^6 \) simplifies to:
\[
\boxed{28r^6k^{10}}
\]