Exponents and Scientific Notation: math test solutions, Grade 8 – download the PDF

1 Evaluating powers / 4 pts

(a) \(2^7 = 128\) (1 pt).

(b) \((-3)^3 = -27\) (1 pt).

(c) \(6^{-2} = \dfrac{1}{36}\) (1 pt).

(d) \(9^0 = 1\) (1 pt).

2 Rules of exponents / 4 pts

(a) \(3^{5+6} = 3^{11}\) (1 pt).

(b) \(10^{12-7} = 10^5\) (1 pt).

(c) \(7^{2 \times 5} = 7^{10}\) (1 pt).

(d) \(2^4 \times (y^3)^4 = 16y^{12}\) (1 pt).

3 Converting numbers / 3 pts

(a) \(3{,}720{,}000 = 3.72 \times 10^6\) (1 pt).

(b) \(0.0000805 = 8.05 \times 10^{-5}\) (1 pt).

(c) \(6.1 \times 10^{-3} = 0.0061\) (1 pt).

4 Operations / 4 pts

(a) \(1.2 \times 5 = 6\) and \(10^{4+3} = 10^7\), so \(6 \times 10^7\) (1 pt).

(b) \(\dfrac{9}{3} \times 10^{8-2} = 3 \times 10^6\) (1 pt).

(c) \(2.5 \times 10^5 = 0.25 \times 10^6\), so the sum is \(5.75 \times 10^6\) (1 pt).

(d) \(7 \times 4 = 28\) and \(10^{-3+(-5)} = 10^{-8}\), so \(28 \times 10^{-8} = 2.8 \times 10^{-7}\) (1 pt).

5 Memory cards / 3 pts

Divide the capacity by the size of one photo (1 pt): \(\dfrac{6.4 \times 10^{10}}{4 \times 10^6} = 1.6 \times 10^{4}\) (1 pt).

About \(16{,}000\) photos fit on the card (1 pt).

6 Hair and bacteria / 2 pts

Divide the widths (1 pt): \(\dfrac{8 \times 10^{-5}}{2 \times 10^{-6}} = 4 \times 10^{1} = 40\). The hair is about 40 times wider than the bacterium (1 pt).