How do you evaluate and simplify #16^(3/2)#?

Question

Eli Assouline · Accepted Answer

See the entire solution process below:

First, we can use this rule of exponents to rewrite this expression: #x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)# #16^(3/2) = 16^(color(red)(1/2) xx color(blue)(3)) = (16^color(red)(1/2))^color(blue)(3)# We can rewrite and simplify this as: #(16^color(red)(1/2))^color(blue)(3) = (sqrt(16))^color(blue)(3) = 4^color(blue)(3)# Now, we can simplify this to: #4^color(blue)(3) = 4 xx 4 xx 4 = 16 xx 4 = 64#

Nathan Axel · Answer

undefined To evaluate and simplify $16^{3/2}$, we can follow these steps:

1. Recognize that $16$ can be expressed as $4^2$.
2. Apply the exponent rule $(a^m)^n = a^{mn}$.
3. Substitute $4^2$ for $16$ and simplify the exponent $\frac{3}{2}$ by multiplying the numerator and denominator by $2$.

The calculation is as follows:

$$ 16^{3/2} = (4^2)^{3/2} = 4^{2 \cdot \frac{3}{2}} = 4^3 = 64 $$

So, $16^{3/2}$ simplifies to $64$.