Represent the following expressions as a power of the number a (a≠0) ((a^2) ^-2) ^5: (a^4a) ^3

a⁻³⁵

Step-by-step explanation:

((a²) ⁻²) ⁵ : (a⁴a) ³

((a²) ⁻²) ⁵ : (a⁴a¹) ³

= (a⁻⁴) ⁵ : (a⁵) ³

= a⁻²⁰ : a¹⁵

= a⁻²⁰⁻¹⁵

= a⁻³⁵

Exponent rules:

Multiplying two numbers with same base: add exponents

Dividing two numbers with same base: subtract exponents

Number with exponent raised to another exponent: multiply the exponents together