Multiplication Properties of Exponents

Front

What is the product of two exponential expressions with the same base?

Back

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

Front

How do you multiply coefficients in expressions with exponents?

Back

To multiply coefficients in expressions with exponents, simply multiply the numerical coefficients together while keeping the variable parts separate. For example, 6 * 4 = 24.

Front

What is the result of multiplying x^a and x^b?

Back

The result is x^(a+b).

Front

What does (ab)^n equal?

Back

(ab)^n = a^n * b^n, meaning you can distribute the exponent to both factors.

Front

What is the power of a product property?

Back

The power of a product property states that (xy)^n = x^n * y^n.

Front

What is the power of a power property?

Back

The power of a power property states that (a^m)^n = a^(m*n).

Front

How do you simplify (5x^2y^2)^3?

Back

You apply the power of a product property: (5^3)(x^(2*3))(y^(2*3)) = 125x^6y^6.

Front

What is the result of (x^5y^3)^4?

Back

Using the power of a power property, the result is x^(5*4)y^(3*4) = x^20y^12.

Front

What happens when you multiply two terms with different bases but the same exponent?

Back

When multiplying two terms with different bases but the same exponent, you can combine them as (a*b)^n = a^n * b^n.

Front

What is the coefficient in the expression 6xy^3?

Back

The coefficient is the numerical factor in the expression, which is 6.