Algebra Annie Applying Exponent Rules

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 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is the product of powers rule?

Back

The product of powers rule states that when multiplying two expressions 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 distribute the exponent to each factor. For example, (ab)^n = a^n * b^n.

Front

What is the quotient of powers rule?

Back

The quotient of powers rule states that when dividing two expressions with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-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 a negative exponent?

Back

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

Front

Simplify: 3a^3 * 9b^6

Back

27a^3b^6.

Front

Simplify: 4y^2 / 3x^4

Back

4y^2 / 3x^4.

Front

Simplify: -10a^4b^3c^3

Back

-10a^4b^3c^3.