Simplify: 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
Answer Details
To simplify this expression, we need to use the rules of exponents:
- 16\(^{\frac{5}{4}}\) can be written as (2\(^4\))\(^{\frac{5}{4}}\) since 16 is equal to 2\(^4\).
- Using the power of a power rule, we can multiply the exponents 4 and 5/4 to get 2\(^5\).
- 2\(^{-3}\) is the same as 1/2\(^3\) or 1/8 since we have a negative exponent.
- 3\(^0\) is equal to 1 since any number raised to the power of 0 is 1.
Therefore, 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\) simplifies to:
(2\(^4\))\(^{\frac{5}{4}}\) x 1/8 x 1
= 2\(^5\) x 1/8
= 32/8
= 4
So the answer is 4.