College Ch 3.1 Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.

Front

Simplify the expression: -5g^6h^4 ⋅ 2gh^3

Back

-10g^7h^7

Front

What is the result of (12x^3y)^2?

Back

144x^6y^2

Front

True or False: The expression x^(1/2) is equivalent to the square root of x.

Back

True

Front

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

Back

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

Front

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

Back

When dividing two powers with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

What does the expression x^(m/n) represent?

Back

The expression x^(m/n) represents the n-th root of x raised to the m-th power, or (n√x)^m.

Front

How do you simplify the expression (x^a)^b?

Back

To simplify (x^a)^b, you multiply the exponents: (x^a)^b = x^(a*b).

Front

What is the value of 8^(1/3)?

Back

The value of 8^(1/3) is 2, since 2^3 = 8.

Front

If a^0 = 1, what is the value of 5^0?

Back

The value of 5^0 is 1.