Question

7/12/20 - Aleks 5 / 13

Simplify without using negative exponents:

(p^-2)/p

(5^-3)^4

Answer 1

The simplified expression of (p^-2)/p(5^-3)^4 without negative exponents is 1/(p^3 * 5^12), obtained by rewriting negative exponents as reciprocals and subtracting like exponents when dividing.

Step-by-step explanation:

To simplify the expression (p^-2)/p(5^-3)^4 without using negative exponents, we need to use the properties of exponents, specifically the rules for division and raising a power to a power.

• First, we address the negative exponents by rewriting them as reciprocals. In this case, p^-2 becomes 1/p^2.
• Next, we simplify (5^-3)^4 by raising the power to the power, which means multiplying the exponents, resulting in 5^-12. Then we rewrite 5^-12 as 1/5^12.
• Now, we have (1/p^2) / (p * 1/5^12). When dividing exponentials, we subtract the exponents of like bases, resulting in 1/(p^3 * 5^12).

Thus, the simplified expression without negative exponents is 1/(p^3 * 5^12).