List of top Mathematics Questions on Laws of Exponents

Evaluate

1. \(\frac{ (8^{−1}× 5^3)}{2^{−4}} \)
2. \((5^{−1}× 2^{−1})×6^{−1}\)

Simplify.

1.  \(\frac{(25×t^{−4})}{(5^{−3}×10×t^{−8})} (t ≠ 0)\)
2. \(\frac{ (3^{−5}×10^{−5}×125)}{(5^{−7}×6^{−5})}\)

Evaluate

1.  {\((\frac{1}{3})^{−1} − (\frac{1}{4})^{−1}\)}⁻¹ 
2.  \((\frac{5}{8})^{−7}× (\frac{8}{5})^{−4}\)

Find the value of m for which (5^m ÷ 5⁻³) = 5⁵

Find the value of

1. (3⁰ × 4⁻¹) × 2² 
2.  (2⁻¹ × 4⁻¹) ÷ 2⁻²
3.  (\(\frac{1}{2}\))⁻² + (\(\frac{1}{3}\))⁻² + (\(\frac{1}{4}\))⁻²
4.  (3⁻¹ +4⁻¹ + 5⁻¹)⁰
5.  {(\(\frac{−2}{3}\))⁻²}²

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

1. (−4) ⁵ ÷ (−4) ⁸ 
2. \(\left(\frac{1 }{ 2^3}\right)\) ² 
3. (−3) ⁴ × (\(\frac{5}{3}\)) ⁴
4. (3 ^-7 ÷ 3 ^-10) × 3 ^-5 
5. 2 ^-3 × (−7) ^-3

Evaluate: 
(i) 3^-2 
(ii) (-4)^-2 
(iii) \((\frac{1}{2})^{-5}\)