Write seven to the five twelfths
power times seven to the three twelfths power in radical form.
We wanna convert these rational
exponents into radical form. To convert rational exponents into
radical form, we use this formula: 𝑥 to 𝑚 over 𝑛 equals the 𝑛 root of 𝑥 to the
𝑚 power. We’re multiplying two exponents
with the same base. This means that our first step here
is to add the two exponents together to simplify. This gives us seven to the eight
But I can actually reduce this
exponent because it’s not a fraction in simplest form. If we divide our numerator and our
denominator by four here, we’re left with seven to the two-thirds power.
Okay. Now we need this guy. In our example, seven to the
two-thirds, our 𝑥 is equal to seven, our 𝑚 is equal to two, and our 𝑛 is equal to
three. The 𝑥-value in our case, seven,
goes inside the radical. The 𝑛-value represents our root,
which in our case is three. And the 𝑚-value for us, two, is
the exponent that’s outside the parentheses.
Radical form of this expression
looks like this: the cube root of seven squared.