Lesson 2 Multiplying Exponents

Front

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

Back

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

Front

How do you multiply a coefficient with a variable raised to an exponent?

Back

Multiply the coefficients together and keep the variable with the exponent. For example, 6k^2 * k = 6 * 1 * k^(2+1) = 6k^3.

Front

What is the result of multiplying 6r and 5r^2?

Back

The result is 30r^3, as you multiply the coefficients (6 * 5) and add the exponents of r (1 + 2).

Front

How do you multiply two variables with the same base?

Back

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

Front

What is the product of 10xy^3 and 8x^5y^3?

Back

The product is 80x^6y^6, as you multiply the coefficients (10 * 8) and add the exponents of x (1 + 5) and y (3 + 3).

Front

What happens when you multiply variables with different bases?

Back

When multiplying variables with different bases, you simply multiply the coefficients and write the variables together. For example, 2a * 3b = 6ab.

Front

What is the result of multiplying 3u^4v^5 and 7u^2v^3?

Back

The result is 21u^(4+2)v^(5+3) = 21u^6v^8.

Front

What is the significance of the exponent in a variable?

Back

The exponent indicates how many times the base is multiplied by itself. For example, x^3 means x * x * x.

Front

How do you simplify the expression 7v^3 * 10u^3v^5?

Back

The simplified expression is 70u^3v^(3+5) = 70u^3v^8.

Front

What is the rule for multiplying exponents with different bases?

Back

When multiplying exponents with different bases, you cannot combine the bases; you simply multiply the coefficients and keep the bases separate.