Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the property of negative integer exponents to the expression 3^(-17)/8^(-14), we can rewrite it as the reciprocal with positive exponents:

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

Now, we can apply the property of negative exponents, which states that a^(-n) = 1/(a^n), where "a" is any non-zero number:

(8^14)/(3^17)

Answer 2

Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To apply the properties of integer exponents, we can simplify the expression (7^(-3))^7 * 7^20 / 6^(-2) with only positive exponents.

First, let's simplify (7^(-3))^7 using the property of power of a power, which states that (a^m)^n = a^(m*n):

(7^(-3))^7 = 7^(-3*7) = 7^(-21)

Now, let's simplify the entire expression using the property of dividing powers with the same base, which states that a^m / a^n = a^(m-n):

(7^(-3))^7 * 7^20 / 6^(-2) = 7^(-21) * 7^20 / 6^(-2)

Next, let's simplify the exponents using the property of multiplying powers with the same base, which states that a^m * a^n = a^(m+n):

= 7^(-21 + 20) / 6^(-2)

= 7^(-1) / 6^(-2)

Finally, let's use the property of negative exponents, which states that a^(-n) = 1 / a^n, to rewrite the expression with positive exponents:

= 1 / 7^1 * 6^2

= 1/7 * 6^2

= 1/7 * 36

= 36/7

So, the answer as an improper fraction is 36/7.

Answer 4

Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7. Show your work and explain how you used the product rule of integer exponents.(2 points)

Answer 5

[AI-generated answer — Bot GPT 3.5]

The product rule of integer exponents states that when multiplying two numbers with the same base, you add the exponents.

To find the numerical equivalent of 12^(-5) * 12^7, we can use the product rule of integer exponents.

First, let's rewrite 12^(-5) as 1/12^5 using the property of negative exponents.

Now we have (1/12^5) * 12^7.

Using the product rule of integer exponents, we add the exponents of 12:

1/12^(5 + 7)

Simplifying the exponent, we have:

1/12^12

To find the numerical equivalent, we can evaluate 12^12:

12^12 = 8,916,100,448

Therefore, the numerical equivalent of 12^(-5) * 12^7 is 1/8,916,100,448.

Answer 6

thanks

Answer 7

[AI-generated answer — Bot GPT 3.5]

You're welcome! If you have any more questions, feel free to ask.