Question

Select the equivalent expression: (2⁻⁴⋅z⁻³)⁵=?

Choose 1 answer:
A. 2z²
B. 2²⁰⋅z¹⁵
C. 1​/2²⁰⋅z¹⁵

Answer 1

The equivalent expression to (2⁻⁴⋅z⁻³)⁵ is 1​/2²⁰⋅z¹⁵, as when we raise a power to a power, we multiply the exponents, and negative exponents can be rewritten as fractions.

Step-by-step explanation:

To select the equivalent expression to (2⁻⁴⋅z⁻³)⁵, we need to apply the rules of exponents. When raising a power to a power, we multiply the exponents. Therefore, we calculate the exponent for 2 as -4 × 5 = -20, and the exponent for z as -3 × 5 = -15, which gives us 2⁻²⁰⋅z⁻¹⁵. We can then rewrite the negative exponents as a fraction, which results in the expression 1​/2²⁰⋅z¹⁵. Hence, the correct answer is C. 1​/2²⁰⋅z¹⁵.