Question

Simplify:

${\displaystyle \frac{{\left(2^5\right)}^2\times 7^3}{8^3\times 7}}$

Answer 1

${\displaystyle \frac{{\left(2^5\right)}^2\times 7^3}{8^3\times 7}}$

= ${\displaystyle \frac{2^{5 \times 2}\times 7^3}{{(2\times 2\times 2)}^3\times 7}}$        ...[∵ (a^m)ⁿ = a^mn]

= ${\displaystyle \frac{2^{10}\times 7^3}{{\left(2^3\right)}^3\times 7}}$

= ${\displaystyle \frac{2^{10}\times 7^3}{2^{3 \times 3}\times 7}}$        ...[∵ (a^m)ⁿ = a^mn]

= ${\displaystyle \frac{2^{10} \times 7^3}{2^9\times 7}}$

= ${\displaystyle 2^{10 - 9}\times 7^{3 - 1}}$       ...(a^m ÷ aⁿ = a^{m - n})

= 2¹ × 7²

= 2 × 7 × 7

= 98