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

What is the error in 3^5 * 3^4 = 9^20?

Back

The error is in misunderstanding the product of powers property; it should be 3^(5+4) = 3^9.

Front

Define the term 'exponent'.

Back

An exponent is a number that indicates how many times to multiply the base by itself.

Front

What is the result of (a^m)^n?

Back

When raising a power to a power, multiply the exponents: (a^m)^n = a^(m*n).

Front

Calculate 7^0.

Back

Any non-zero number raised to the power of 0 is 1, so 7^0 = 1.