Multiplication Properties of Exponents

Front

What is the product of powers property of exponents?

Back

When multiplying two expressions with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify (2x^3y)^6?

Back

You apply the power of a product property: (ab)^n = a^n * b^n. Thus, (2^6)(x^(3*6))(y^6) = 64x^18y^6.

Front

What is the sum of exponents property of exponents?

Back

When multiplying like bases, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify a^2(a^3)(a^6)?

Back

You add the exponents: a^(2+3+6) = a^11.

Front

What is the product of powers property when applied to (9w^2x^8)(w^6x^4)?

Back

You add the exponents for like bases: 9w^(2+6)x^(8+4) = 9w^8x^12.

Front

How do you simplify (6cd^5)(5c^5d^2)?

Back

Multiply the coefficients and add the exponents for like bases: 6*5 = 30, c^(1+5) = c^6, d^(5+2) = d^7, resulting in 30c^6d^7.

Front

What is the power of a power property of exponents?

Back

When raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

How do you simplify (-3y)^3?

Back

You apply the power of a product property: (-3)^3 * y^3 = -27y^3.

Front

What is the zero exponent rule?

Back

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

A negative exponent indicates the reciprocal: a^(-n) = 1/(a^n).