Simplifying Exponents

Front

What is the definition of an exponent?

Back

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Front

What is the product rule for exponents?

Back

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

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify an expression with a negative exponent?

Back

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

Front

What is the power of a power rule for exponents?

Back

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

Front

How do you simplify (ab)^n?

Back

Using the power of a product rule, (ab)^n = a^n * b^n.

Front

What is the value of 2^3?

Back

2^3 = 2 * 2 * 2 = 8.

Front

How do you simplify the expression (8y^3)^6?

Back

Using the power of a power rule: (8^6)(y^(3*6)) = 8^6y^18.

Front

What is the result of multiplying two expressions with different bases but the same exponent?

Back

If a and b are different bases, a^n * b^n = (ab)^n.

Front

How do you simplify the expression -4r^5 * 2r^8?

Back

Multiply the coefficients and add the exponents: -4 * 2 = -8 and 5 + 8 = 13, so the result is -8r^13.