Simplifying Exponents Flashcard

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 x 2 x 2.

Front

What does it mean to simplify an expression with exponents?

Back

Simplifying an expression with exponents means to reduce it to its simplest form, often by applying the laws of exponents.

Front

What is the product of powers rule?

Back

The product of powers rule states that when multiplying two powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the power of a power rule?

Back

The power of a power rule states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

What is the power of a product rule?

Back

The power of a product rule states that when raising a product to a power, you can distribute the exponent to each factor. For example, (ab)^n = a^n * b^n.

Front

What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, a^0 = 1, where a ≠ 0.

Front

What is the negative exponent rule?

Back

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n), where a ≠ 0.

Front

Simplify: 3^2 * 3^3

Back

3^2 * 3^3 = 3^(2+3) = 3^5 = 243.

Front

Simplify: (2^4)^2

Back

(2^4)^2 = 2^(4*2) = 2^8 = 256.

Front

Simplify: (xy)^3

Back

(xy)^3 = x^3 * y^3.