Mixed Exponent Rules

Front

What is the rule for changing a negative exponent to a positive exponent?

Back

To change a negative exponent to a positive exponent, take the reciprocal of the base. For example, x^(-n) = 1/(x^n).

Front

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

Back

Any non-zero number raised to the power of zero is equal to 1. For example, (xyz)^0 = 1.

Front

Simplify: 1/x^(-3)

Back

x^3

Front

Simplify: x^(-6)

Back

1/x^6

Front

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

Back

When multiplying two powers with the same base, add the exponents. For example, x^a * x^b = x^(a+b).

Front

Simplify: -3xy^3 * (4xy)^2

Back

-48x^3y^5

Front

What is the power of a product rule?

Back

The power of a product rule states that (ab)^n = a^n * b^n.

Front

Simplify: (x^2y)^5

Back

x^10y^5

Front

What is the quotient of powers rule?

Back

When dividing two powers with the same base, subtract the exponents. For example, x^a / x^b = x^(a-b).

Front

What happens when you raise a power to another power?

Back

When raising a power to another power, multiply the exponents. For example, (x^a)^b = x^(a*b).