Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)6⋅ 51710−2

Question

with only positive exponents, then solve the expression. (1 point)
(5−3)6⋅ 51710−2=

Answer 1

Applying the property of integer exponents, we know that (a^b)^c = a^(b*c). Therefore, we can rewrite (5^-3)^6 as 5^(-3*6).

Now, multiplying 517^1 and 10^-2, we use the property a^m * a^n = a^(m + n). This gives us 517^1 * 10^-2 = 517^(1-2) = 517^-1.

Therefore, the equivalent expression is 5^(-3*6) * 517^-1.

To solve this expression, we need to evaluate the exponents.

First, we simplify 5^(-3*6) = 5^-18. Using the property a^(-n) = 1/(a^n), we can rewrite this as 1/(5^18).

Now, we simplify 517^-1 = 1/517.

Therefore, the simplified expression is (1/(5^18)) * (1/517).

To compute this expression, we multiply the numerators and denominators separately:

(1 * 1) / (5^18 * 517)
= 1 / (5^18 * 517)

The final result is 1 / (5^18 * 517).