Question

What is the value of (9⁻⁵)(p⁴)³ x (p⁻4)(q³)⁰ expression when p=3 and q=-9?

A) 1/729


B) 729


C) 1/243


D) 243

Answer 1

The value of the expression (9⁻⁵)(p⁴)³ x (p⁻⁴)(q³)⁰ when p=3 and q=-9 is 1/729, corresponding to Choice A). This involves applying exponent rules and substituting given values of p and q.

Step-by-step explanation:

To find the value of the expression (9⁻⁵)(p⁴)³ x (p⁻⁴)(q³)⁰ when p=3 and q=-9, follow these steps:

1. Remember that any number raised to the zero power is 1, so (q³)⁰ = 1.
2. Apply the power rule, which states that (x⁴)³ = x⁴׳, so (p⁴)³ = p¹².
3. Multiply exponents with the same base by adding them and invert the base with negative exponents (9⁻⁵) is the same as 1/9⁵.
4. Substitute the values of p and q into the expression.
5. Simplify the expression step-by-step to get the final result.

By performing these operations, we find the expression simplifies to 1/729, which corresponds to Choice A).