Exponents - 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.

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 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 distribute the exponent to each factor: (ab)^n = a^n * b^n.

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: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

The negative exponent rule 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 (3x^3)(4x^-2)?

Back

To simplify (3x^3)(4x^-2), multiply the coefficients (3*4) and add the exponents of x (3 + (-2)): 12x^(3-2) = 12x.

Front

What is the simplified form of (2a^2b^4z)(6a^3b^2z^5)?

Back

To simplify (2a^2b^4z)(6a^3b^2z^5), multiply the coefficients (2*6) and add the exponents for each variable: 12a^(2+3)b^(4+2)z^(1+5) = 12a^5b^6z^6.

Front

How do you simplify x * x^7 * x^3?

Back

To simplify x * x^7 * x^3, add the exponents: 1 + 7 + 3 = 11. The simplified form is x^11.

Front

What is the simplified form of (2x^4y^7)^3?

Back

To simplify (2x^4y^7)^3, apply the power of a product property: (2^3)(x^(4*3))(y^(7*3)) = 8x^12y^21.