Answer:
[tex]B = \frac{1}{3}[/tex]
[tex]C = 16[/tex]
[tex]E = 4096[/tex]
Step-by-step explanation:
Given
[tex]A^B * C^D = E^F[/tex] --- Missing from the question
[tex]2*4 = 8[/tex]
[tex]A = 8[/tex]
[tex]D = \frac{1}{2}[/tex]
[tex]F = \frac{1}{4}[/tex]
Required: Find B, C and E
Substitute values for A, D and F in [tex]A^B * C^D = E^F[/tex]
[tex]8^B * C^{\frac{1}{2}} = E^{\frac{1}{4}}[/tex]
Compare the above expression to: [tex]2*4 = 8[/tex]
We have:
[tex]8^B = 2[/tex]
[tex]C^{\frac{1}{2}} = 4[/tex]
[tex]E^{\frac{1}{4}} = 8[/tex]
In [tex]8^B = 2[/tex]
Express 8 as a 2^3
[tex]2^{3B }= 2^1[/tex]
Cancel out 2
[tex]3B = 1[/tex]
[tex]B = \frac{1}{3}[/tex]
In [tex]C^{\frac{1}{2}} = 4[/tex]
Express 4 as [tex]16^{\frac{1}{2}}[/tex]
[tex]C^{\frac{1}{2}} = 16^{\frac{1}{2}}[/tex]
The exponents cancel out
[tex]C = 16[/tex]
In [tex]E^{\frac{1}{4}} = 8[/tex]
Express 8 as [tex]4096^{\frac{1}{4}}[/tex]
[tex]E^{\frac{1}{4}} = 4096^{\frac{1}{4}}[/tex]
The exponents cancel out
[tex]E = 4096[/tex]
