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.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent a/b to radical form, write it as the b-th root of a raised to the power of a: x^(a/b) = b√(x^a).

Front

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

Back

Any non-zero number raised to the power of zero is always equal to 1.

Front

What is the simplified form of (x^m)^n?

Back

The simplified form is x^(m*n), which is obtained by multiplying the exponents.

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the quotient of powers property?

Back

The quotient of powers property states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

How do you simplify the expression 5^(3) * 5^(2)?

Back

You can simplify it using the product of powers property: 5^(3+2) = 5^5.

Front

What is the value of (5^3 * x^2 * y^4)^0?

Back

The value is 1, since any expression raised to the power of zero equals 1.

Front

What is the value of 16^(1/2)?

Back

The value is 4, since the square root of 16 is 4.

Front

How do you express the cube root of x in exponential form?

Back

The cube root of x can be expressed as x^(1/3).