Laws of Exponents

Front

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

Back

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

Front

What is the result of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero is equal to 1: a^0 = 1 (where a ≠ 0).

Front

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

Back

To simplify (x^m)(x^n), add the exponents: (x^m)(x^n) = x^(m+n).

Front

What is the power of a power rule in exponents?

Back

The power of a power rule states that to raise a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

Front

How do you simplify a^m / a^n?

Back

To simplify a^m / a^n, subtract the exponents: a^m / a^n = a^(m-n).

Front

What is the result of multiplying two powers with different bases but the same exponent?

Back

When multiplying two powers with different bases but the same exponent, you can multiply the bases and keep the exponent: a^n * b^n = (a*b)^n.

Front

What is the value of 5^3 * 5^4?

Back

5^3 * 5^4 = 5^(3+4) = 5^7.

Front

How do you express (y^8)^5 in exponential notation?

Back

Using the power of a power rule, (y^8)^5 = y^(8*5) = y^40.

Front

What is the sum of the exponents when multiplying 3^4 and 3^7?

Back

3^4 * 3^7 = 3^(4+7) = 3^11.

Front

What does n^0 equal for any non-zero n?

Back

n^0 = 1 for any non-zero n.