Answer:
Step-by-step explanation:
Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.
Examples
(a) ![(p^4)^{\dfrac{3}{2}}](https://tex.z-dn.net/?f=%28p%5E4%29%5E%7B%5Cdfrac%7B3%7D%7B2%7D%7D)
From above, we have a power to a power, so, we can think of multiplying the exponents.
i.e.
![(p^{^ {\dfrac{4}{1}}})^{\dfrac{3}{2}}](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B4%7D%7B1%7D%7D%7D%29%5E%7B%5Cdfrac%7B3%7D%7B2%7D%7D)
![(p^{^ {\dfrac{12}{2}}})](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B12%7D%7B2%7D%7D%7D%29)
Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.
SO;
![(p^{^ {\dfrac{12}{2}}})](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B12%7D%7B2%7D%7D%7D%29)
![= (p^{ 6})](https://tex.z-dn.net/?f=%3D%20%28p%5E%7B%206%7D%29)
Let's take a look at another example
![\Bigg (27x^{^\Big{6}} \Bigg) ^{{\dfrac{5}{3}}}](https://tex.z-dn.net/?f=%5CBigg%20%2827x%5E%7B%5E%5CBig%7B6%7D%7D%20%5CBigg%29%20%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D)
Here, we apply the
to both 27 and ![x^6](https://tex.z-dn.net/?f=x%5E6)
![= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{6}{1}\times {{\dfrac{5}{3}}} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%2827%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%5Ctimes%20x%5E%5CBig%7B%5Cdfrac%7B6%7D%7B1%7D%5Ctimes%20%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%7D%5CBigg%29)
![= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{2}{1}\times {{\dfrac{5}{1}}} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%2827%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%5Ctimes%20x%5E%5CBig%7B%5Cdfrac%7B2%7D%7B1%7D%5Ctimes%20%7B%7B%5Cdfrac%7B5%7D%7B1%7D%7D%7D%20%7D%5CBigg%29)
Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.
∴
![= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%28%5Csqrt%5B3%5D%7B27%7D%5E%7B5%7D%20%5Ctimes%20x%5E%7B10%7D%20%7D%5CBigg%29)
![= \Bigg (3^{5} \times x^{10} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%283%5E%7B5%7D%20%5Ctimes%20x%5E%7B10%7D%20%7D%5CBigg%29)
![= 249x^{10}](https://tex.z-dn.net/?f=%3D%20249x%5E%7B10%7D)
Cylinder Volume
V = hπr²
154 cm³ = 16 cm × 3.14 × r²
154 cm³ = 50.28 cm × r²
r² = 154 cm³ : 50.28 cm
r² = 3.0625 cm²
r = 1.75 cm
d = 2r
d = 2 × 1.75 cm
d = 3.5 cm
So, the diameter of the Cylinder is 3.5 cm
#LearnWithEXO
Answer: i love brinly its the best
the value of x is 4, make m||n
Step-by-step explanation:
sorry if this is wrong
Answer:
Hi there!
The answer is;
585 miles per 13 hours
Step-by-step explanation:
270 miles per 6 hours
/6 to determine miles per hour
45 miles per 1 hour
× 13 to determine miles per 13 hours
585 miles per 13 hours
Hope this helps!