Answer:
(x⁻² x⁻³)⁴ = x⁻¹⁴
Explanation:
To simplify the expression (x⁻² x⁻³)⁴, you can start by using the product rule of exponents which states that when you multiply two powers with the same base, you can add their exponents.
So, you can rewrite the expression as:
(x⁻² x⁻³)⁴ = x⁻²⁺³⁴ x⁻³⁺³⁴
Next, simplify the exponents:
x⁻²⁺³⁴ x⁻³⁺³⁴ = x⁻⁸ x⁻⁶ = x⁻⁸⁺⁶ = x⁻¹⁴
Therefore, (x⁻² x⁻³)⁴ = x⁻¹⁴.
To simplify other expressions with exponents, you can use the exponent laws such as:
Product rule: aⁿ aᵐ = aⁿᵐ
Quotient rule: aⁿ / aᵐ = aⁿ⁻ᵐ
Power rule: (aⁿ)ᵐ = aⁿᵐ
You can also use the order of operations (PEMDAS) to simplify expressions with exponents, just as you would with other mathematical expressions.