Fractional Exponents and its Radical Forms

Front

What is a fractional exponent?

Back

A fractional exponent represents both a power and a root. For example, x^(1/n) is the nth root of x.

Front

How do you convert a fractional exponent to a radical form?

Back

The expression x^(m/n) can be written as the nth root of x raised to the m power: √[n]{x^m}.

Front

What is the rule for multiplying expressions with the same base?

Back

When multiplying expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the rule for dividing expressions with the same base?

Back

When dividing expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

What happens when you raise a power to another power?

Back

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

Front

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

Back

16^(1/2) = √16 = 4.

Front

What is the value of 27^(2/3)?

Back

27^(2/3) = (√[3]{27})^2 = 3^2 = 9.

Front

How do you simplify 4^(3/2)?

Back

4^(3/2) = (√4)^3 = 2^3 = 8.

Front

What is the value of 64^(1/3)?

Back

64^(1/3) = √[3]{64} = 4.

Front

What is the rule for raising a product to a power?

Back

When raising a product to a power, you apply the exponent to each factor: (ab)^n = a^n * b^n.