Question

Simplify and express the result in power notation with positive exponent.

(3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵

Answer 1

(3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵

= `[3^(-7-(-10))] xx 3^-5`           ...[∵ a^m × aⁿ = a^{m − n}]

= `[3^(−7+10) × 3^(−5)]`

= `3^3 xx 3^-5 = 3^(3+(-5))`          ...[∵ a^m × aⁿ = a^{m + n}]

= `3^(3-5) = 3^-2 = 1/(3)^2`           ...`[∵ a^-m = 1/a^m]`