1.4 Rational Exponents

Essential standard I can convert radical expressions and rational exponents I can use properties of exponents to combine radicals

RATIONAL EXPONENTS Any radical expression can be written in an equivalent form using fractional (rational) exponents instead of the radical sign. 36 = 36 1 2 3 64 = 64 1 3 4 16 = 16 1 4 The index is the denominator of the exponent. The exponent is the numerator of the exponent.

PROBLEM 1 What is the simplified form of each expression? A) 216 1 3

PROBLEM 2 Convert between exponential and radical form. A) What is 𝑥 3 7 in radical form? B) What is 𝑎 5 and 5 𝑏 3 in exponential form?

POWER RULES The main advantage of changing a radical into exponential form is it allows the use of power rules, which are shortcuts for exponents.

PROBLEM 3 Rewrite in radical form 4 𝑥 3 8 𝑥 2

SIMPLIFYING RATIONAL EXPONENTS The index is the denominator of the exponent. The exponent is the numerator of the exponent. With a rational exponent, there are two operations to perform instead of one. 4 3 2 means we must raise 4 to the third power ( 4 3 ) and square root it ( 4 1 2 = 4 )

PROBLEM 4 What is −32 4 5 in simplest form?

PROBLEM 5 Simplify each expression. A) 𝑥 2 3 ⋅ 𝑥 5 6 B) 𝑥 3 7 ÷ 𝑥 5 14

GOT IT? below Simplify each expression. A) 𝑦 2 5 ⋅ 𝑦 3 10 B) 𝑥 4 9 ÷ 𝑥 1 3

Essential standard I can convert radical expressions and rational exponents I can use properties of exponents to combine radicals