Laws of exponents Problem set A

Write \((3x^2)^3 \times 2x^{-5}\) in the form \(ax^p\).

Find the exact value of:

1. (a) \(2^{-5}\).
2. (b) \(\left(\frac{3}{4}\right)^{-2}\).

Write \(\frac{(5x^2)^2}{10x^{-3}}\) in the form \(ax^p\).

Find the exact value of:

1. (a) \(4^{-3}\);
2. (b) \(\left(\frac{2}{5}\right)^{-3}\);
3. (c) \(5^0 + 3^{-1}\).

Write each answer in the form \(a\times10^{k}\).

1. (a) Write 0.000 047 2 in standard form.
2. (b) Find \((4.5\times10^{6})\times(8\times10^{-9})\).
3. (c) Find \((7.2\times10^{8})+(5\times10^{9})\).
4. (d) Find \(\dfrac{9\times10^{-3}}{1.5\times10^{-8}}\).

The brightness of a lamp is \(B = 80d^{-2}\) lux at a distance of d metres. Find the exact brightness at a distance of:

1. (a) \(d = \frac{2}{5}\) m;
2. (b) \(d = 4\) m.

The number of bacteria in a dish, in thousands, is \(N = 3 \times 2^t\), where t is the time in hours after noon. A negative t means before noon. Find the exact number of thousands of bacteria:

1. (a) 4 hours after noon;
2. (b) 3 hours before noon.

The mass of the Earth is \(5.97\times10^{24}\) kg and the mass of the Moon is \(7.35\times10^{22}\) kg.

1. (a) Find their total mass, in the form \(a\times10^{k}\).
2. (b) How many times greater is the mass of the Earth than the mass of the Moon? Give your answer to 3 significant figures.

Write \(\frac{(3x^{-2})^2 \times 8x^3}{6x^{-4}}\) in the form \(ax^p\).