Question

Express as a power of a rational number with negative exponent.

(2⁵ ÷ 2⁸) × 2^–7 

Answer 1

Using laws of exponents,

a^m ÷ aⁿ = a^{m – n}

And a^m × aⁿ = a^{m + n}  ...[∵ a is non-zero integer]

∴ (2⁵ ÷ 2⁸) × 2^–7  = (2^{5 – 8}) × 2^–7 

= 2^–3 × 2^–7

= 2^{–3 – 7}

= 2^–10