# Exponent properties with quotients review

Review the quotient of powers and power of a quotient properties, and then try some practice problems.

## Quotient of powers property

The quotient of powers property states that when we divide two powers with the same base, we subtract the exponents.
start fraction, a, start superscript, m, end superscript, divided by, a, start superscript, n, end superscript, end fraction, equals, a, start superscript, m, minus, n, end superscript, a, does not equal, 0
Example
start fraction, 4, start superscript, 7, end superscript, divided by, 4, start superscript, 3, end superscript, end fraction, equals, 4, start superscript, 7, minus, 3, end superscript, equals, 4, start superscript, 4, end superscript
start fraction, start color blueD, 4, start superscript, 7, end superscript, end color blueD, divided by, start color greenD, 4, start superscript, 3, end superscript, end color greenD, end fraction, equals, start fraction, start color blueD, 4, end color blueD, dot, start color blueD, 4, end color blueD, dot, start color blueD, 4, end color blueD, dot, start color blue, 4, end color blue, dot, start color blueD, 4, end color blueD, dot, start color blueD, 4, end color blueD, dot, start color blueD, 4, end color blueD, divided by, start color greenD, 4, end color greenD, dot, start color greenD, 4, end color greenD, dot, start color greenD, 4, end color greenD, end fraction
empty space, equals, start color blue, 4, end color blue, dot, start color blueD, 4, end color blueD, dot, start color blueD, 4, end color blueD, dot, start color blue, 4, end color blue
empty space, equals, 4, start superscript, 4, end superscript

## Power of a quotient property

The power of a quotient property states that when we raise a quotient to a power, we raise both the numerator and the denominator to the power.
left parenthesis, start fraction, a, divided by, b, end fraction, right parenthesis, start superscript, m, end superscript, equals, start fraction, a, start superscript, m, end superscript, divided by, b, start superscript, m, end superscript, end fraction, b, does not equal, 0
Example
left parenthesis, start fraction, 2, divided by, 5, end fraction, right parenthesis, start superscript, 4, end superscript, equals, start fraction, 2, start superscript, 4, end superscript, divided by, 5, start superscript, 4, end superscript, end fraction
left parenthesis, start fraction, 2, divided by, 5, end fraction, right parenthesis, start superscript, 4, end superscript, equals, start fraction, 2, divided by, 5, end fraction, dot, start fraction, 2, divided by, 5, end fraction, dot, start fraction, 2, divided by, 5, end fraction, dot, start fraction, 2, divided by, 5, end fraction
empty space, equals, start fraction, 2, dot, 2, dot, 2, dot, 2, divided by, 5, dot, 5, dot, 5, dot, 5, end fraction
empty space, equals, start fraction, 2, start superscript, 4, end superscript, divided by, 5, start superscript, 4, end superscript, end fraction