What is an exponent?

An exponent indicates how many times a base is multiplied by itself. For example, in 3², the base is 3 and the exponent is 2, which means 3 * 3 = 9.

What is the rule for multiplying powers with the same base?

To multiply powers with the same base, add the exponents. 
For Example, 
2³ * 2² 
= 2⁽³⁺²⁾ = 2⁵ = 32.

What is the rule for dividing powers with the same base?

To divide powers with the same base, subtract the exponents. 
For Example, 
7⁵ / 7² 
= 7^(5-2) = 7³ = 343.

What is the value of 5⁰?

Any non-zero number raised to the power of zero equals 1. Therefore, 5⁰ = 1.

Simplify the expression: (4²)³.

To simplify a power raised to another power, multiply the exponents: 
(4²)³ 
= 4^(2*3) = 4⁶
= 4096.

If 2^x = 16, what is x? Hint: Express 16 as a power of 2.

Since 16 = 2⁴, we have 
2^x = 2⁴, 
which implies x = 4.

What is the formula for the power of a product? Provide an example.

The power of a product states that (ab)ⁿ = aⁿbⁿ. For Example, 
(2 * 3)² 
= 2² * 3² 
= 4 * 9 
= 36.

What is a negative exponent? Give an example.

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. 
For Example, 
3⁻² 
= 1/(3²) 
= 1/9.

Find the value of x if 10^2x = 100. 

(Hint: Rewrite 100 as a power of 10)

Since 100 = 10², 
we have 10^2x = 10², which implies 2x = 2, and therefore x = 1.

Simplify: (x³ * y²)²

Using the power of a product, 
(x³ * y²)²
= x^(3*2) * y^(2*2)
= x⁶ * y⁴.

If 3^x * 3² = 3⁵, what is the value of x? 

(Hint: Use the property of exponents for multiplication)

Using the property 
a^m * aⁿ = a^(m+n), 
we have 3^(x+2) = 3⁵, which implies x + 2 = 5, so x = 3.