Rational Number and Exponents Grade VIII with solutions

Worksheet

1. Question: Rachna purchased \(2 \frac{1}{2}\) kg onions at ₹10 per kg and \(1 \frac{3}{8}\) kg potatoes at ₹\(16 \frac{8}{11}\) per kg. She gave a five hundred rupee note to the shopkeeper. Find the amount she got back from the shopkeeper.

   Solution: Total cost of onions = \(2 \frac{1}{2}\) kg x ₹10 = ₹25

   Total cost of potatoes = \(1 \frac{3}{8}\) kg x ₹\(16 \frac{8}{11}\) = ₹\(1 \frac{3}{8}\) x \(16.7273\) ≈ ₹23.64

   Total cost = ₹25 + ₹23.64 ≈ ₹48.64

   Amount Rachna got back = ₹500 - ₹48.64 = ₹451.36

2. Question: Simplify \((512)^{\left(-\frac{2}{3}\right)}\).

   Solution: \((512)^{\left(-\frac{2}{3}\right)} = \left(\sqrt[3]{512}\right)^{-2} = (8^{-2}) = \frac{1}{64}\).

3. Question: Find the value of \(x\).

   (a) \( \sqrt[3]{5x + 2} = 2 \)

   Solution: \( 5x + 2 = 2^3 \Rightarrow 5x + 2 = 8 \Rightarrow 5x = 6 \Rightarrow x = \frac{6}{5} \).

   (b) \(5^{x-1} \times 3^{2x-5} - 225\)

   Solution: It appears that the equation is incomplete. Please check the equation again.

4. Question: Write in standard form

   (a) 0.0000000777

   Solution: \(7.77 \times 10^{-8}\).

   (b) \(234.45 \times 10^{12}\)

   Solution: \(2.3445 \times 10^{14}\).

5. Question: Evaluate \(\left[\left(\frac{-2}{3}\right)^{-2} - \left(\frac{-3}{4}\right)^{-1} \right] \times \left(\frac{3}{2}\right)^2\).

   Solution: \(\left[\left(\frac{-2}{3}\right)^{-2} - \left(\frac{-3}{4}\right)^{-1} \right] \times \left(\frac{3}{2}\right)^2 = \left[\left(\frac{3}{2}\right)^2 - \left(\frac{4}{3}\right) \right] \times \frac{9}{4} = \left[\frac{9}{4} - \frac{4}{3} \right] \times \frac{9}{4} = \left(\frac{27}{12} - \frac{16}{12}\right) \times \frac{9}{4} = \frac{11}{4} \times \frac{9}{4} = \frac{99}{16}\).