Powers and roots: solved examples

Worked examples of powers and roots, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

Example 1. Work out $5^2$ .
1. Multiply 2 copies of 5. $5^2 = 5 \times 5 = 25$
Answer: $25$
Example 2. Work out $3^3$ .
1. Multiply 3 copies of 3. $3^3 = 3 \times 3 \times 3 = 27$
Answer: $27$
Example 3. Work out $14^2$ .
1. Multiply 2 copies of 14. $14^2 = 14 \times 14 = 196$
Answer: $196$

Example 4. Work out $\sqrt{49}$ .
1. Find the number whose square is this. $7^2 = 49$
2. So the root is $\sqrt{49} = 7$
Answer: $7$
Example 5. Work out $\sqrt[3]{64}$ .
1. Find the number whose cube is this. $4^3 = 64$
2. So the root is $\sqrt[3]{64} = 4$
Answer: $4$
Example 6. Work out $\sqrt{361}$ .
1. Find the number whose square is this. $19^2 = 361$
2. So the root is $\sqrt{361} = 19$
Answer: $19$

Example 7. Write $5^{6} \times 5^{4}$ as a single power of 5. What is the new power?
1. Add the powers. $5^{6} \times 5^{4} = 5^{6 + 4} = 5^{10}$
Answer: $10$
Example 8. Write $2^{2} \times 2^{6}$ as a single power of 2. What is the new power?
1. Add the powers. $2^{2} \times 2^{6} = 2^{2 + 6} = 2^{8}$
Answer: $8$
Example 9. Work out $10^{0}$ . Give your answer as a fraction or a whole number.
1. Any non-zero number to the power 0 is 1. $10^{0} = 1$
Answer: $1$

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