Laws of exponents Problem set B

Write \((2x^3)^4 \times 5x^{-9}\) in the form \(ax^p\).

Find the exact value of:

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

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

Find the exact value of:

1. (a) \(5^{-3}\);
2. (b) \(\left(\frac{3}{2}\right)^{-3}\);
3. (c) \(7^0 - 2^{-2}\).

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

1. (a) Write 0.000 061 3 in standard form.
2. (b) Find \((3.5\times10^{7})\times(6\times10^{-10})\).
3. (c) Find \((8.4\times10^{7})+(3\times10^{8})\).
4. (d) Find \(\dfrac{1.2\times10^{-2}}{4\times10^{-9}}\).

The strength of a Wi-Fi signal is \(S = 54d^{-2}\) units at a distance of d metres from the router. Find the exact strength at a distance of:

1. (a) \(d = \frac{3}{2}\) m;
2. (b) \(d = 6\) m.

The area of mould on a wall, in cm², is \(M = 5 \times 3^t\), where t is the time in days after it was first measured. A negative t means before it was first measured. Find the exact area:

1. (a) 3 days after it was measured;
2. (b) 2 days before it was measured.

One drive in a data centre stores \(4.2\times10^{12}\) bytes and a second drive stores \(8.5\times10^{11}\) bytes.

1. (a) Find the total number of bytes stored, in the form \(a\times10^{k}\).
2. (b) How many times more does the first drive store than the second? Give your answer to 3 significant figures.

Write \(\frac{(2x^{-3})^3 \times 9x^7}{12x^{-5}}\) in the form \(ax^p\).