Exponent Rules Algebra

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).

Front

What does it mean to rewrite an expression using positive exponents?

Back

Rewriting an expression using positive exponents means converting any negative exponents into positive ones by taking the reciprocal of the base. For example, x^(-n) = 1/(x^n).

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

How do you simplify x^4 * y^(-2) * x^(-2) * y^2?

Back

You combine like bases by adding the exponents: x^(4-2) * y^(-2+2) = x^2 * y^0 = x^2.

Front

What is the result of (3x^4y^5)^2?

Back

Using the power of a product rule, you get 3^2 * (x^4)^2 * (y^5)^2 = 9x^8y^{10}.

Front

How do you rewrite 2w^(-13) using a positive exponent?

Back

You rewrite it as 2/(w^13).

Front

What is the value of 10 in the equation 2^x = 1024?

Back

The value of x is 10 because 2^10 = 1024.