Exponents: Product of Powers

Front

What is the Product of Powers Property?

Back

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

Front

If 2^3 * 2^2 = ?

Back

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

Front

What mistake did Billy make in 3^5 * 3^4 = 9^20?

Back

He incorrectly multiplied the exponents instead of adding them.

Front

What is the area of a rectangle with length 4a^4b^5 and width 3a^2b^3?

Back

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

Front

What is the value of 5^0?

Back

Any non-zero number raised to the power of 0 is 1. So, 5^0 = 1.

Front

How do you simplify (x^3)^4?

Back

Use the power of a power property: (x^3)^4 = x^(3*4) = x^12.

Front

What is the result of 7^2 * 7^3?

Back

7^(2+3) = 7^5 = 16807.

Front

If a^m * a^n = a^5, what can you say about m and n?

Back

m + n = 5.

Front

What is the base in the expression 4^3?

Back

The base is 4.

Front

What is the exponent in the expression 10^2?

Back

The exponent is 2.