Final Review Practice: Exponents and Natural Base e

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).

Tags

CCSS.6.EE.A.1

Front

What does it mean to simplify an expression with exponents?

Back

Simplifying an expression with exponents means to rewrite it in a simpler form, often by combining like terms and ensuring all exponents are positive.

Tags

CCSS.8.EE.A.1

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add their exponents. For example, a^m * a^n = a^(m+n).

Tags

CCSS.8.EE.A.1

Front

What is the quotient of powers property?

Back

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

Tags

CCSS.8.EE.A.1

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Tags

CCSS.8.EE.A.1

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).

Tags

CCSS.8.EE.A.1

Front

What is the natural base e?

Back

The natural base e is an irrational number approximately equal to 2.71828, and it is the base of the natural logarithm. It is used in exponential growth and decay models.

Front

How do you express exponential growth?

Back

Exponential growth can be expressed with the function y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you express exponential decay?

Back

Exponential decay can be expressed with the function y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Tags

CCSS.HSF-IF.C.8B