Respuesta :
The expression Y=16 x 10^8k, in terms of k , for y^5/4 is [tex]y^{\frac{5}{4} } =32(10^{10k} )[/tex].
What is exponents?
The term "exponent" describes how many times any number is multiplied. Power is the result of multiplying a number by itself a predetermined number of times.
In order to define a number's power as a full expression, a value is raised to an exponent.
RULE 1: Zero Property
Any real number that is not zero when it is multiplied by zero will equal 1.
e.g; [tex]x^{0}=1[/tex]
RULE 2: Negative Property
Any real number that is not zero that is raised to a minus power will be equal to one divide by the same number that is raised to a positive power.
e.g; [tex]X^{(-a)}=\frac{1}{\left[X^{(a)}\right]}[/tex]
RULE 3: Product Property
The answer is the total of the exponent that have the same base while multiplied 2 exponent that have the same nonnegative real number base.
e.g; [tex]X^{(a) *} X^{(b)}=X^{(a+b)}[/tex]
RULE 4: Power of a Power Property
You can multiply exponents if one exponential is raised to a higher exponent.
e.g; [tex]\left(X^{(a)}\right)^{(b)}=X^{(a b)}[/tex]
RULE 5: Power of a Product Property
If the sum of two positive number real figures is being brought up to an exponent, the exponent can be divided among the factors and each one multiplied separately.
e.g; [tex](X Y)^{(a)}=X^{(a)} * Y^{(a)}[/tex]
Calculation for the given expression;
The given equation is;
[tex]y=16 \times 10^{8 k}[/tex]
Raise the power (5/4) on both side of the expression.
[tex]y^{(5 / 4)}=\left(16 \times 10^{8 k}\right)^{5 / 4}[/tex]
Now, use rule 5.
[tex]y^{5 / 4}=16^{5 / 4} \times 10^{8 k.5 / 4}[/tex]
Further solve the equation by using rule 4.
[tex]y^{5 / 4}=2^{5 } \times 10^{8 k.5 / 4}\\y^{5 / 4}=32\times 10^{2 k.5 }\\y^{5 / 4}=32\times 10^{10 k}\\[/tex]
Therefore, the simplification of the expression is [tex]y^{\frac{5}{4} } =32(10^{10k} )[/tex].
To know more about exponent rules, here
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