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.

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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).

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).

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.

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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).

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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).

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.

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

Back

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

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.

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).