Properties of Exponents: Product and Power

Front

What is the product of two powers with the same base?

Back

To multiply two powers with the same base, add their exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify the expression (ab^m)(ab^n)?

Back

To simplify (ab^m)(ab^n), multiply the coefficients and add the exponents of like bases: a^(1+1)b^(m+n) = a^2b^(m+n).

Front

What is the power of a product rule?

Back

The power of a product rule states that (ab)^n = a^n * b^n.

Front

How do you simplify (x^m)^n?

Back

To simplify (x^m)^n, multiply the exponents: (x^m)^n = x^(m*n).

Front

What is the result of 4^5 * 4?

Back

4^5 * 4 = 4^(5+1) = 4^6.

Front

What is the product of coefficients in the expression (6p^2q^3)(4pq)?

Back

The product of coefficients is 6 * 4 = 24.

Front

How do you simplify the expression (4x^5)(6x^2)?

Back

Multiply the coefficients (4 * 6 = 24) and add the exponents of x (5 + 2 = 7): (4x^5)(6x^2) = 24x^7.

Front

What is the simplified form of (-3x^4)(5x^2)?

Back

Multiply the coefficients (-3 * 5 = -15) and add the exponents of x (4 + 2 = 6): (-3x^4)(5x^2) = -15x^6.

Front

What is the result of (4x^5)^2?

Back

(4x^5)^2 = 4^2 * (x^5)^2 = 16x^(5*2) = 16x^10.

Front

What happens when you multiply two powers with different bases?

Back

When multiplying two powers with different bases, you cannot combine them; you simply write them as a product: a^m * b^n.