Exponents and Rational Exponents

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is a rational exponent?

Back

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

Front

What does x^(1/n) represent?

Back

x^(1/n) represents the nth root of x. For example, x^(1/3) is the cube root of x.

Front

What is the value of 81^(-3/4)?

Back

1/27. The negative exponent indicates a reciprocal, and the fractional exponent indicates a root.

Front

What is the solution to x^(2/3) = -9?

Back

No real solution, because a real number raised to a fractional exponent cannot be negative.

Front

How do you simplify (6x-3)^(2/3) + 6 = 15?

Back

First, isolate (6x-3)^(2/3) to find x. The solutions are x = 5 and x = -4.

Front

What is the simplified form of 16^(1/4)?

Back

2, because the fourth root of 16 is 2.

Front

What is the product of x^(a) * x^(b)?

Back

x^(a+b). When multiplying like bases, add the exponents.

Front

What is the quotient of x^(a) / x^(b)?

Back

x^(a-b). When dividing like bases, subtract the exponents.

Front

What is the power of a power rule?

Back

(x^a)^b = x^(a*b). When raising a power to another power, multiply the exponents.