Welcome to the mind-stretching world of indices and roots! Get ready to exercise those maths muscles and put your knowledge of exponents and square roots to the test. This is no ordinary maths quiz; it's an expedition designed to sharpen your mind and make your grey cells dance with numbers. Are you ready to embark on this intrepid journey into the mathematical universe? Don't worry; our helpful comments are quite useful. Let's begin!

1.

What is 10^{2}?

100

10

20

1000

10 to the power of 2 means 10 multiplied by itself (10 x 10), which equals 100.

2.

Simplify: 5^{3} x 5^{2}

5^{6}

5^{5}

10^{5}

25^{5}

When multiplying terms with the same base, you add the exponents. Therefore, 5^{3} x 5^{2} becomes 5^{(3+2)} or 5^{5}.

3.

Simplify: (√ 64 )^{2}

64

32

16

8

The square root of 64 is 8, and when you square it again (8 x 8), it becomes 64.

4.

What is the cube root of 27?

6

5

3

9

The cube root of 27 is 3 because 3 x 3 x 3 = 27.

5.

What is the square root of 25?

5

2

6

4

The square root of 25 is 5 because 5 x 5 = 25.

6.

If 2^{n} = 16, what is the value of n?

4

8

2

6

The value of n is 4 because 2 raised to the power of 4 (2 x 2 x 2 x 2) equals 16.

7.

What is 2^{3} x 2^{2}?

2^{6}

2^{7}

2^{5}

2^{4}

When multiplying terms with the same base, you add the exponents. Therefore, 2^{3} x 2^{2} becomes 2^{(3+2)} or 2^{5}.

8.

What is 4^{5}?

1,024

256

512

64

4 to the power of 5 means 4 multiplied by itself 5 times (4 x 4 x 4 x 4 x 4), which equals 1,024.

9.

What is the square root of 81?

10

9

8

11

Square root of 81 is 9 because 9 x 9 = 81.

10.

If 3^{n} = 27, what is the value of n?

6

3

9

5

The value of n is 3 because 3 raised to the power of 3 (3 x 3 x 3) equals 27.