Question

Please help me I really stuck

Answer 1

Explanation:

y^(5/4) = (16×10^(8k))^(5/4)

remember all the rules of exponents :

an exponent of an exponent : we multiply both exponents.

x^(a/b) =

`\sqrt[b]{ {x}^(a) } = ({ \sqrt[b]{x} })^(a)`

and

(a×b)^c = a^c × b^c

so, with that we can do the trick here :

y^(5/4) = (16×10^(8k))^(5/4) =

= 16^(5/4) × 10^(8k × 5/4)

16^(5/4) =

`\sqrt[4]{ {16}^(5) } = ( \sqrt[4]{16} )^(5) = ( \sqrt[4]{ {2}^(4) })^(5) = {2}^(5) = 32`

10^(8k × 5/4) = 10^(40k/4) = 10^(10k)

so, the result is

32 × 10^(10k)

`32 * {10}^(10k)`

Answer 2

We can find the value of Y when k = 5/4 by substituting k = 5/4 in the given expression for Y:

Y = 16 × 10^8 × k

Y = 16 × 10^8 × (5/4)

Y = 20 × 10^8

To express this in standard form, we can convert it to scientific notation:

Y = 2.0 × 10^9