Unit 3 - Day 5 Do Now: Exponent Rules

Front

What is the rule for simplifying expressions with negative exponents?

Back

The rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, x^(-n) = 1/(x^n).

Front

What is any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero equals 1. For example, a^0 = 1, where a ≠ 0.

Front

How do you simplify the expression x^4 * x^12?

Back

To simplify, you add the exponents: x^4 * x^12 = x^(4+12) = x^16.

Front

What is the product of two terms with the same base?

Back

When multiplying two terms with the same base, you add their exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify the expression (6x^2)(-3x^5)?

Back

Multiply the coefficients and add the exponents of the like bases: (6 * -3) * (x^2 * x^5) = -18x^(2+5) = -18x^7.

Front

What is the value of 3^0?

Back

The value of 3^0 is 1, as any non-zero number raised to the power of zero equals 1.

Front

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

Back

When dividing expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression (a^m)^n?

Back

To simplify, you multiply the exponents: (a^m)^n = a^(m*n).

Front

What happens when you raise a product to a power, such as (ab)^n?

Back

When raising a product to a power, you raise each factor to that power: (ab)^n = a^n * b^n.

Front

What is the rule for raising a quotient to a power, such as (a/b)^n?

Back

When raising a quotient to a power, you raise both the numerator and the denominator to that power: (a/b)^n = a^n / b^n.