Using the laws of exponents, $a^m \times a^n = a^{m+n}$. Here, $3^2 \times 3^4 = 3^{2+4} = 3^6$. Therefore, the correct option is $3^6$.

Prime factorization of 64 gives $2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6$. Therefore, the correct option is $2^6$.

Question 1

What is the value of $2^3$?

Accepted Answer

To find the value of $2^3$, we multiply the base 2 by itself three times: $2 	imes 2 	imes 2 = 8$. Therefore, the correct option is 8.

Question 2

Evaluate $3^2 	imes 3^4$.

Accepted Answer

Using the laws of exponents, $a^m 	imes a^n = a^{m+n}$. Here, $3^2 	imes 3^4 = 3^{2+4} = 3^6$. Therefore, the correct option is $3^6$.

Question 3

What is the value of $a^0$ for any non-zero integer $a$?

Accepted Answer

Any non-zero integer raised to the power of zero is equal to 1. Therefore, $a^0 = 1$. The correct option is 1.

Question 4

Simplify: $5^4 \div 5^2$.

Accepted Answer

Using the law of exponents for division, $a^m \div a^n = a^{m-n}$. Thus, $5^4 \div 5^2 = 5^{4-2} = 5^2$. The correct option is $5^2$.

Question 5

Express 64 as a power of 2.

Accepted Answer

Prime factorization of 64 gives $2 	imes 2 	imes 2 	imes 2 	imes 2 	imes 2 = 2^6$. Therefore, the correct option is $2^6$.

Exponents and Powers