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. But please don't put slashes or special characters....

Answer 1

To rewrite the expression without slashes or special characters, we'll start with the given expression:

(7^(-4) / 8^6)^(-2) * (7^(-3) / 8^9)

We can simplify this step by step:

1. Apply the negative exponent to both terms inside the parentheses:

   (7^(-4))^(-2) / (8^6)^(-2) * (7^(-3) / 8^9)

   This gives us:

   7^(8) / 8^(-12) * 7^(-3) / 8^9

2. Rewrite the expression using the property of negative exponents for 8^(-12), which means 1 / 8^12:

   7^8 * (1 / 8^12) * 7^(-3) / 8^9

   This simplifies to:

   7^8 * 7^(-3) / (8^12 * 8^9)

3. Combine the powers of 7:

   7^(8 - 3) / (8^12 * 8^9) = 7^5 / (8^12 * 8^9)

4. Combine the powers of 8:

   7^5 / (8^(12 + 9)) = 7^5 / 8^21

5. Final expression without slashes or special characters:

7 to the power of 5 over 8 to the power of 21

So, the equivalent expression you requested is:

7 to the power of 5 over 8 to the power of 21

Answer 2

AND HOW DID YOU KNOW? I don't need no more special characters or slashes.

Answer 3

I apologize for misunderstanding your request earlier. Here’s the equivalent expression without any slashes or special characters:

7 to the power of 5 divided by 8 to the power of 21

If you need any further help, feel free to ask!

Answer 4

No, you were right the first time. But how did you know the answer?

Answer 5

I arrived at the answer by applying the laws of exponents systematically. Here's a breakdown of the process:

1. Understanding Negative Exponents:

   • Any expression with a negative exponent can be rewritten as the reciprocal of that expression with a positive exponent. For example, \( a^{-n} = \frac{1}{a^n} \).

2. Applying Power of a Power Rule:

   • When raising a power to another power, you multiply the exponents. That is, \( (a^m)^n = a^{m \cdot n} \).

3. Combining Exponents:

   • When multiplying two exponential terms with the same base, you can add the exponents. That is, \( a^m \cdot a^n = a^{m+n} \).

4. Consolidating Terms:

   • After applying these rules, I combined all similar bases (in this case, both \( 7 \) and \( 8 \)), simplified, and reorganized the final expression.

By following these steps methodically, I was able to simplify and arrive at the final equivalent expression. If you have any more questions about exponent rules or need clarification on any step, feel free to ask!

Answer 6

Answer this question correctly without slashes, and work this out!

Answer 7

Sure! Let's work through the given expression step-by-step without using slashes.

Starting expression:
(7 raised to the power of negative 4 divided by 8 raised to the power of 6) raised to the power of negative 2 times 7 raised to the power of negative 3 divided by 8 raised to the power of 9

Step 1: Apply the negative exponent to the term inside the parentheses.

Using the rule that (a/b) raised to the power of n = a raised to the power of n divided by b raised to the power of n:

(7 raised to the power of negative 4) raised to the power of negative 2 divided by (8 raised to the power of 6) raised to the power of negative 2

Step 2: Simplify each part.

First, simplify (7 raised to the power of negative 4) raised to the power of negative 2:

7 raised to the power of negative 4 times negative 2 equals 7 raised to the power of 8

Next, simplify (8 raised to the power of 6) raised to the power of negative 2:

8 raised to the power of 6 times negative 2 equals 8 raised to the power of negative 12

Putting this together, we have:

7 raised to the power of 8 divided by 8 raised to the power of negative 12

Step 3: Rewrite the negative exponent.

Rewrite 8 raised to the power of negative 12 as 1 divided by 8 raised to the power of 12:

7 raised to the power of 8 times 1 divided by 8 raised to the power of 12

So now, we have:

7 raised to the power of 8 times 1 divided by 8 raised to the power of 12

Step 4: Now incorporate the second part of the original expression.

Next, we need to multiply by (7 raised to the power of negative 3 divided by 8 raised to the power of 9):

Continuing from our expression, we multiply by:

7 raised to the power of negative 3 divided by 8 raised to the power of 9:

So, the expression now looks like:

(7 raised to the power of 8 times 1 divided by 8 raised to the power of 12) times (7 raised to the power of negative 3 divided by 8 raised to the power of 9)

Step 5: Combine everything.

We can combine the powers of 7 and the powers of 8:

Numerator: 7 raised to the power of 8 times 7 raised to the power of negative 3 equals 7 raised to the power of (8 plus negative 3) which simplifies to 7 raised to the power of 5.

Denominator: 8 raised to the power of 12 times 8 raised to the power of 9 equals 8 raised to the power of (12 plus 9) which simplifies to 8 raised to the power of 21.

Final expression:

7 raised to the power of 5 divided by 8 raised to the power of 21

Therefore, the correct answer is:

7 raised to the power of 5 over 8 raised to the power of 21

If you have any further questions or need additional assistance, please let me know!