apply the property of negative integer exponent to generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only

Question

apply the property of negative integer exponent to generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

To apply the property of negative integer exponent, we can rewrite the expression by moving the negative exponents to the denominator and changing their signs.

The expression 3^(-17) divided by 8^(-14) is equivalent to (1/3^17) divided by (1/8^14).

To convert the negative exponent to positive, we take the reciprocal of the base.

So, the expression can be rewritten as (1/(3^17)) divided by (1/(1^14 x 8^14)).

Since any number raised to the power of 1 is equal to the number itself, we can simplify further to get:

1/(3^17) divided by (1/(8^14)).

Finally, when we divide by a fraction, we multiply by the reciprocal of that fraction.

Therefore, the expression is equivalent to (1/(3^17)) times (8^14).

So, the expression with positive exponents only is 8^14 divided by 3^17.

Answer 2

Step-by-Step Bot answered
1 year ago

To apply the property of negative integer exponents and obtain an expression equivalent to \(3^{-17} \div 8^{-14}\) with positive exponents only, we can reciprocate both terms and change the signs of the exponents. Starting with the given expression:

\(3^{-17} \div 8^{-14}\)

By reciprocating both terms, we get:

\(\frac{1}{3^{17}} \div \frac{1}{8^{14}}\)

To change the signs of the exponents, we can rewrite the expression as:

\(\frac{8^{14}}{3^{17}}\)

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

Answer 3

Explain Bot answered
1 year ago

To apply the property of negative integer exponents and generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only, you can follow these steps:

1. Start with the given expression:

3^(-17) / 8^(-14)

2. Apply the property of negative exponents, which states that a number raised to a negative exponent can be rewritten as its reciprocal raised to the positive exponent.

Rewrite 3^(-17) as 1 / 3^17 and rewrite 8^(-14) as 1 / 8^14.

Now our expression becomes:

(1 / 3^17) / (1 / 8^14)

3. When dividing fractions, you can multiply the numerator by the reciprocal of the denominator.

In this case, instead of dividing by 1 / 8^14, we can multiply by the reciprocal, which is 8^14 / 1.

The expression becomes:

(1 / 3^17) * (8^14 / 1)

4. Simplify the expression by multiplying the numerators together and the denominators together.

The numerator is 1 * 8^14 = 8^14, and the denominator is 3^17.

The simplified expression is:

8^14 / 3^17

Therefore, the expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only is 8^14 / 3^17.