What is an exponent?

An exponent indicates how many times a number, known as the base, is multiplied by itself. For example, in 2³, 2 is the base and 3 is the exponent, meaning 2 * 2 * 2 = 8.

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

When multiplying exponents with the same base, add the exponents. For example, a² * a³ = a^{(2 + 3)} = a⁵.

How do you simplify the expression 4^(3/2)?

The expression 4^(3/2) can be simplified by rewriting it as (√4)³. Since √4 = 2, we have 2³ = 8.

Solve for x: 2^x = 32.

Hint: Express 32 as a power of 2.

We can rewrite 32 as 2⁵. Thus, 2^x = 2⁵, which means x = 5.

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

When dividing exponents with the same base, subtract the exponents. For example, a⁵ / a² = a^{(5 - 2)} = a³.

What is the value of 3⁰?

Any non-zero number raised to the power of 0 is 1. Therefore, 3⁰ = 1.

How do you express the square root of a number using exponents?

The square root of a number x can be expressed as x^(1/2). For example, √9 = 9^(1/2) = 3.

If x = 4, what is the value of x² + 2x?

Substituting x = 4 gives us 4² + 2(4) = 16 + 8 = 24.

Simplify: (x²y³)².

Hint: Apply the power of a product rule.

Using the power of a product rule, (x²y³)² = x^(2*2)y^(3*2) = x⁴y⁶.

What is the product of 5⁽²⁾ and 5⁽³⁾?

Using the multiplication rule, 5² * 5³ = 5^{(2 + 3)} = 5⁵.