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 5^0?

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: (x^3 * y^2)².

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

If 3^x * 3^2 = 3^5, what is the value of x? Hint: Use the property of exponents for multiplication.

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