Find the product. (i) a² × (2a²²) × (4a²⁶) (ii) (2/3xy) × (-9/10x²y²) (iii) (-1/3pq³) × (6/5p³q) (iv) x × x² × x × x³ × x⁴

As we know that when the exponential terms get multiplied with the same bases, then we can add their powers as i.e., am × an = a(m+n). (1)
This is also known as product law/rule
(i) a² × (2a²²) × (4a²⁶) = (2 × 4)(a² + 22 + 26) [from equation (1)] = 8a⁵⁰
∴ a² × (2a²²) × (4a²⁶) = 8a⁵⁰
(ii) (2/3xy) × (-9/10x²y²) = 2 × (-9)/3 × 10 × x(1+2) × y(1+2) [from equation(1)] = -3/5x³y³
∴ (2/3xy) × (-9/10x²y²) = -3/5x³y³
(iii) (-1/3pq³) × (6/5p³q) = (-1) × 6/3 × 5 × p1+3 × q3+1 [from equation (1)] = -2/5p⁴q⁴
∴ (-1/3pq³) × (6/5p³q) = -2/5p⁴q⁴
(iv) x × x² × x × x³ × x⁴ = x1+2+1+3+4 [from equation (1)] = x¹¹
∴ x × x² × x × x³ × x⁴ = x¹¹