Simplify 3√4 × 3√16 using properties of exponents
Answers
Step-by-step explanation:
Radical expressions can also be written without using the radical symbol. We can use rational (fractional) exponents. The index must be a positive integer. If the index \displaystyle nn is even, then \displaystyle aa cannot be negative.
\displaystyle {a}^{\frac{1}{n}}=\sqrt[n]{a}a
n
1
=
n
√
a
We can also have rational exponents with numerators other than 1. In these cases, the exponent must be a fraction in lowest terms. We raise the base to a power and take an nth root. The numerator tells us the power and the denominator tells us the root.
\displaystyle {a}^{\frac{m}{n}}={\left(\sqrt[n]{a}\right)}^{m}=\sqrt[n]{{a}^{m}}a
n
m
=(
n
√
a
)
m
=
n
√
a
m
All of the properties of exponents that we learned for integer exponents also hold for rational exponents.