Exponents and Exponent Rules

These flashcards cover key concepts and rules related to exponents as discussed in the lecture.

What is the result of multiplying two negative fives inside parentheses?

Positive 25.

What does the expression -5 squared equal?

Negative 25.

What is the first exponent rule?

a^m times a^n = a^(m+n) when multiplying with the same base.

When multiplying x^4 by x^3, what happens to the exponents?

You add the exponents to get x^(4+3) = x^7.

What is the result of 2² times 2⁴?

2⁶, which equals 64.

In the expression (a^m)/(a^n), what happens to the exponents?

You subtract the exponents: a^(m-n).

What happens when you have a base raised to a power outside parentheses, e.g., (xy)^n?

You apply the exponent to each part: x^n * y^n.

What is the rule when raising a power to another power, e.g., (a^m)^n?

You multiply the exponents: a^(m*n).

What does a negative exponent, such as a^-n, represent?

It represents one over the positive exponent: 1/(a^n).

What is the value of any base raised to the zero power, e.g., a^0?

One (1).

If you have a negative sign outside parentheses with a base raised to zero, what is the result?

The result is the negative value of the base raised to zero.

How do you simplify an expression like 8^11 / 8^9?

You subtract the exponents to get 8^(11-9) = 8^2.

What is the result of (2 over 5)^3?

2^3 over 5^3, which simplifies to 8 over 125.

When simplifying x^3 * x^(-5), what is the final result?

1 / x^2, since the negative exponent moves it to the denominator.

What is the relationship between negative exponents and the placement of numbers in fractions?

Negative exponents indicate that the base should move between the numerator and denominator.