Write an equivalent expression for the given expression.

Question

open parentheses 7 to the power of negative 4 end exponent over 8 to the power of 6 close parentheses to the power of negative 2 end exponent times 7 to the power of negative 3 end exponent over 8 to the power of 9

Answer 1

We start with the expression:

\[ \left( \frac{7^{-4}}{8^6} \right)^{-2} \cdot \frac{7^{-3}}{8^9} \]

First, we simplify \( \left( \frac{7^{-4}}{8^6} \right)^{-2} \).

Using the property of exponents that \( (a/b)^{-n} = \frac{b^n}{a^n} \), we have:

\[ \left( \frac{7^{-4}}{8^6} \right)^{-2} = \frac{(8^6)^2}{(7^{-4})^2} = \frac{8^{12}}{7^{-8}} = \frac{8^{12}}{\frac{1}{7^8}} = 8^{12} \cdot 7^8 \]

Now substituting back into our expression:

\[ 8^{12} \cdot 7^8 \cdot \frac{7^{-3}}{8^9} \]

Now we combine the terms:

1. For the \( 7 \) terms:

\[ 7^8 \cdot 7^{-3} = 7^{8 + (-3)} = 7^{5} \]

2. For the \( 8 \) terms:

\[ 8^{12} \cdot 8^{-9} = 8^{12 + (-9)} = 8^{3} \]

Putting it all together, we obtain:

\[ \frac{7^5}{8^3} \]

Therefore, the equivalent expression is:

\[ \frac{7^5}{8^3} \]

Answer 2

no slashes, please...

Answer 3

Sure! Let's write the equivalent expression without using slashes.

We started with:

\[ \left( \frac{7^{-4}}{8^6} \right)^{-2} \cdot \frac{7^{-3}}{8^9} \]

We simplified this to:

\[ 8^{12} \cdot 7^{8} \cdot 8^{-9} \cdot 7^{-3} \]

Which we combined into:

1. For the \( 7 \) terms: \[ 7^{8} \cdot 7^{-3} = 7^{5} \]

2. For the \( 8 \) terms: \[ 8^{12} \cdot 8^{-9} = 8^{3} \]

So, combining both results, the equivalent expression is:

\[ 7^{5} \text{ over } 8^{3} \]

Or simply stated without slashes:

7 to the power of 5 over 8 to the power of 3.

Answer 4

NO SLASHES!!!!!!

Answer 5

I apologize for misunderstanding your request. Here's the expression written without slashes:

7 to the power of 5 multiplied by 8 to the power of negative 3.

Thank you for your patience!