Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only

Answer 1

[AI-generated answer — Bot GPT 3.5]

Using the property of negative integer exponents, we can convert the expression to positive exponents as follows:

3^-17/8^-14

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

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

Thus, the expression with positive exponents only is 8^14/3^17.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To apply the property of negative integer exponents, we can move negative exponents to the denominator and change their sign to positive.

Starting with the expression 3^-17/8^-14, we can rewrite it as:

1 / (3^17 × 1/8^14)

Now, to get rid of the negative exponents, we can move the base to the opposite side of the fraction and change the sign of the exponent to positive:

8^14 / 3^17

Therefore, an expression equivalent to 3^-17/8^-14 with positive exponents only is 8^14 / 3^17.

Answer 3

[AI-generated answer — Explain Bot]

To apply the Property of Negative Integer Exponents, we use the rule:

𝑎^−𝑛 = 1 / 𝑎^𝑛

Let's start by expressing the given expression with positive exponents using this rule:

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

Since 3 is the base of the first term, and 8 is the base of the second term, we can rewrite the expression as:

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

Now, let's simplify further by applying the division rule:

1 / 3^17 * 8^14

According to the rule of multiplication of exponents, we can rewrite this expression as:

8^14 / 3^17

Therefore, the expression equivalent to 3^(-17) / 8^(-14) with positive exponents only is 8^14 / 3^17.