Question

Apply the Properties of Integer Exponents to generate an equivalent expression to (5^−3)6⋅ 5^17/10^−2 (1 point)
a. 1/20
b. 20
c. 1/500
d. 500

Answers

Answered by Damon
where did the 6 go bot?
Answered by Damon
I think there is a typo in the problem statement but can not guess what it should be. 5^17 is simply a ridiculous number.
Answered by GPT 3.5
To generate an equivalent expression, we can use the property of integer exponents that states a^m ÷ a^n = a^(m-n).

So, we can rewrite the expression as:

(5^(-3+17))/(10^-2)

Simplifying the exponents, we get:

= 5^14 / 10^-2

Now, using the property of integer exponents again, we can rewrite this as:

= 5^14 × 10^2

Finally, simplifying the expression, we have:

= (5^2)^(14/2) × 10^2

= 25^7 × 10^2

= 50^7

Therefore, the equivalent expression is 50^7.

The answer is not provided in the options given.
Answered by GPT 3.5
Apologies for missing that step.

We have:

(5^(-3))6 × 5^17 / 10^(-2)

First, let's simplify the negative exponents:

1/(5^3) × 6 × 5^17 / (1/(10^2))

Now, let's simplify the fractions:

6 × (5^17) × (10^2) / (5^3)

Using the property of integer exponents, we can rewrite (5^17) as (5^3) × (5^14):

6 × (5^3) × (5^14) × (10^2) / (5^3)

Now, cancel out the common factors:

6 × (5^14) × (10^2)

Since (10^2) equals 100, we can rewrite the expression as:

6 × (5^14) × 100

Finally, we can combine the constants:

600 × (5^14)

Therefore, the equivalent expression is 600 × (5^14).

The answer is not provided in the options given.
Answered by GPT 3.5
I apologize for any confusion caused by the incorrect exponent. Given that the exponent 5^17 is not feasible, it seems there may indeed be a typo or mistake in the problem statement. Without the correct information, it is not possible to generate an equivalent expression.

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