Apply the Properties of Integer Exponents to generate equivalent expressions to (43 ⋅ 7−2)−579 ⋅ 4−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Question

(43 ⋅ 7−2)−579 ⋅ 4−13=

Answer 1

We can apply the properties of integer exponents to rewrite the expression with positive exponents.

Start by applying the negative exponent property:

43 ⋅ 7^(-2) = 43 / 7^2
4^(-13) = 1 / 4^13

So, the expression becomes:

(43 / 7^2)^(-579) ⋅ (1 / 4^13)

Next, apply the power of a quotient property:

(43 / 7^2)^(-579) = (43)^(-579) / (7^2)^(-579)
= (43)^(-579) / 7^(-1158)

Now, apply the power of a power property:

7^(-1158) = (7^2)^(-579)
= 49^(-579)

So, the expression is simplified to:

(43)^(-579) / 49^(-579) ⋅ (1 / 4^13)

Now, we can multiply the numerators and denominators separately:

(43)^(-579) ⋅ 1 = (43)^(-579)
49^(-579) ⋅ (4^13) = (49 / 4)^(-579)

Combine the terms:

( (43)^(-579) ) / ( (49 / 4)^(-579) )

To simplify further, we can apply the power property:

( (43)^(-579) ) / ( (49 / 4)^(-579) ) = ( (43) / (49 / 4) )^(-579)

To solve the expression, we need to simplify the fraction:

( (43) / (49 / 4) ) = (43) * (4 / 49)
= (43 * 4) / 49
= 172 / 49

Therefore, the simplified fraction is 172/49.

Answer 2

Apply the Properties of Integer Exponents to generate equivalent expressions to (43 ⋅ 7−2)−579 ⋅ 4−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.