Law of Exponents

Front

What is the base in an exponential expression?

Back

The base is the number that is raised to a power in an exponential expression, such as in 2³ where 2 is the base.

Front

How do you express repeated multiplication using exponents?

Back

Repeated multiplication can be expressed using exponents. For example, 4 x 4 x 4 x 4 x 4 x 4 can be written as 4⁶.

Front

What is a negative exponent and how can it be converted to a positive exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, 9^-3 can be converted to 1/9³.

Front

What is the product of powers property in exponents?

Back

The product of powers property states that when multiplying two expressions with the same base, you add the exponents. For example, (x³)(x²) = x⁵.

Front

How do you expand an expression with exponents?

Back

To expand an expression with exponents, you multiply the base by itself as many times as indicated by the exponent. For example, x⁵ expands to x ⋅ x ⋅ x ⋅ x ⋅ x.

Front

What is the quotient of powers property in exponents?

Back

The quotient of powers property states that when dividing two expressions with the same base, you subtract the exponents. For example, x⁵ / x² = x³.

Front

What is the power of a power property in exponents?

Back

The power of a power property states that when raising an exponent to another exponent, you multiply the exponents. For example, (x²)³ = x⁶.

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, 5⁰ = 1.

Front

How do you simplify expressions with negative exponents?

Back

To simplify expressions with negative exponents, convert them to positive exponents by taking the reciprocal of the base. For example, a^-n = 1/aⁿ.

Front

What is the significance of the exponent in an exponential expression?

Back

The exponent indicates how many times the base is multiplied by itself. For example, in 3⁴, the exponent 4 means 3 is multiplied by itself 4 times.