Exponents: Product of Powers

Front

What is the product of powers property?

Back

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

Front

Calculate the area of a rectangle with length 4a^4b^5 and width 3a^2b^3.

Back

Area = length ⋅ width = 4a^4b^5 * 3a^2b^3 = 12a^(4+2)b^(5+3) = 12a^6b^8.

Front

What is the value of 2^3 * 2^2?

Back

2^3 * 2^2 = 2^(3+2) = 2^5 = 32.

Front

If x^4 * x^3 = x^n, what is the value of n?

Back

n = 4 + 3 = 7.

Front

What happens when you multiply powers with different bases?

Back

You cannot combine them using the product of powers property; you must multiply the bases separately.

Front

What is 5^2 * 5^3?

Back

5^2 * 5^3 = 5^(2+3) = 5^5 = 3125.

Front

If a^m * a^n = a^5, what is m + n?

Back

m + n = 5.

Front

What is the result of (3^2)^3?

Back

(3^2)^3 = 3^(2*3) = 3^6 = 729.

Front

What is the product of 7^4 and 7^1?

Back

7^4 * 7^1 = 7^(4+1) = 7^5 = 16807.

Front

What is the area of a rectangle with length 2x^3 and width 5x^2?

Back

Area = 2x^3 * 5x^2 = 10x^(3+2) = 10x^5.