Indices and Cube Root (घातांक आणि घनमूळ) MCQ Test — Class 8 Maharashtra SSC

Solution:

Using the law $a^m \times a^n = a^{m+n}$:

$2^3 \times 2^4 = 2^{3+4}$ — = 2^7

Solution:

By definition, any non-zero number raised to the power 0 is 1.

$a^0 = 1$ for all $a \neq 0$ — 5^0 = 1

Solution:

Using the law $(a^m)^n = a^{mn}$:

$(3^2)^3 = 3^{2 \times 3}$ — = 3^6

Solution:

By definition, $a^{-n} = \frac{1}{a^n}$:

$2^{-3} = \frac{1}{2^3}$ — = \frac{1}{8}

Solution:

Using the law $\frac{a^m}{a^n} = a^{m-n}$:

$\frac{7^5}{7^3} = 7^{5-3}$ — = 7^2

Solution:

$10000 = 10 \times 10 \times 10 \times 10$ — = 10^4

Solution:

When $-1$ is raised to an even power, the result is $1$.

Since 50 is even: — (-1)^{50} = 1

Solution:

$4^2 \times 4^{-2} = 4^{2+(-2)} = 4^0$ — = 1

Solution:

$0.001 = \frac{1}{1000} = \frac{1}{10^3}$ — = 10^{-3}

Solution:

$(2 \times 3)^2 = 6^2$ — = 36

Or equivalently: $2^2 \times 3^2 = 4 \times 9 = 36$