Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3 rasied to the power of −17/8 rasied to the power of −14 with positive exponents only.(1 point) 3 rasied to the power of −17/8 rasied to the power of −14=

Answer 1

To apply the property of negative integer exponents and rewrite the expression \(3^{-\frac{17}{8}}^{-14}\) with positive exponents, we can use the rule that states \(a^{-b} = \frac{1}{a^b}\).

Here's how we can transform the given expression step by step:

1. Rewrite the expression using the negative exponent property:

   \[ 3^{-\frac{17}{8}}^{-14} = 3^{\left(-\frac{17}{8} \cdot -14\right)} \]

2. Multiply the exponents:

   \[ -\frac{17}{8} \cdot -14 = \frac{17 \cdot 14}{8} = \frac{238}{8} \]

3. Simplify the fraction:

   \[ \frac{238}{8} = \frac{119}{4} \]

4. Rewrite with positive exponents:

   Therefore, we have:

   \[ 3^{-\frac{17}{8}}^{-14} = 3^{\frac{119}{4}} \]

So, the expression equivalent to \(3^{-\frac{17}{8}}^{-14}\) with positive exponents only is:

\[ 3^{\frac{119}{4}} \]

Answer 2

i dont under stand the answer could you do it in word form

Answer 3

Of course! Let’s break it down step by step in a more detailed way using words.

1. Start with the expression: We have the expression where we are looking at the number 3 raised to the power of negative \( \frac{17}{8} \) raised to the power of negative 14.

2. Understand the rules about negative exponents: A negative exponent means we take the reciprocal. For example, \( a^{-b} \) is equal to \( \frac{1}{a^b} \).

3. Apply the negative exponent rule: When we raise a number to a negative exponent, we can rewrite it as the reciprocal of that number raised to the corresponding positive exponent. So, if we see \( 3^{-\frac{17}{8}} \), it can be rewritten as \( \frac{1}{3^{\frac{17}{8}}} \).

4. Combine the exponents: We also have another exponent, which is negative 14. The expression becomes more complicated because we are raising to another exponent. Specifically, when we have something like \( A^{-B} \), it becomes \( \left( A^{-B} \right) = 3^{-\frac{17}{8}} \) raised to the power of negative 14. This means we can multiply the two negative exponents together.

5. Multiply the two negative exponents: When we multiply the negative fraction \( -\frac{17}{8} \) by negative 14, we find that the negatives cancel out, resulting in a positive exponent. We multiply \( -\frac{17}{8} \) by -14, which can be thought of as:

   • First, multiplying just the numbers: \( 17 \times 14 \) equals 238.
   • Then, we divide that by 8, resulting in \( \frac{238}{8} \).
   • After simplifying, \( \frac{238}{8} \) gives us \( \frac{119}{4} \).

6. Rewrite the original expression: Finally, instead of having two negative exponents, we now have a positive exponent. So, the original expression \( 3^{-\frac{17}{8}}^{-14} \) can now be rewritten simply as \( 3^{\frac{119}{4}} \).

In summary, the original expression \( 3^{-\frac{17}{8}}^{-14} \) can be rewritten in positive exponents as \( 3^{\frac{119}{4}} \).

I hope this explanation makes it clearer! Let me know if you have any other questions.