Exponents & Exponent Properties

Front

What is an exponent?

Back

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

Tags

CCSS.6.EE.A.1

Front

What is the product of powers property?

Back

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

Tags

CCSS.8.EE.A.1

Front

What is the power of a product property?

Back

The power of a product property states that when raising a product to a power, you can distribute the exponent to each factor: (ab)^n = a^n * b^n.

Tags

CCSS.8.EE.A.1

Front

What is the zero exponent property?

Back

The zero exponent property states that any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Tags

CCSS.8.EE.A.1

Front

What is the negative exponent property?

Back

The negative exponent property states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Tags

CCSS.8.EE.A.1

Front

How do you simplify c^4 ⋅ c^3?

Back

You apply the product of powers property: c^4 ⋅ c^3 = c^(4+3) = c^7.

Tags

CCSS.8.EE.A.1

Front

What is the simplified form of 4^(-2)?

Back

Using the negative exponent property, 4^(-2) = 1/(4^2) = 1/16.

Tags

CCSS.8.EE.A.1

Front

How do you simplify (2a^2b^4z)(6a^3b^2z^5)?

Back

You multiply the coefficients and add the exponents for like bases: (2*6)(a^(2+3))(b^(4+2))(z^(1+5)) = 12a^5b^6z^6.

Tags

CCSS.HSA.APR.A.1

Front

What is the quotient of powers property?

Back

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

Tags

CCSS.8.EE.A.1