a - 8
Step-by-step explanation:
[tex] {8}^{y} = {16}^{y + 2} \\ \\ \therefore \: {2}^{3y} = {2}^{4(y + 2)} \\ \\ \therefore \: {2}^{3y} = {2}^{4y + 8} \\ \\ \therefore \: 3y = 4y + 8 \\ \\ \therefore \: 3y - 4y = 8 \\ \\ \therefore \: - y = 8 \\ \\ \therefore \: y = - 8[/tex]
If 8 Superscript y Baseline = 16 Superscript y + 2 = -8.
Exponents of numbers exist added when the numbers exist multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent:
[tex]$a^{m} \times a^{n}=a^{m+n} ; a^{m} \div a^{n}=a^{m-n} ;\left(a^{m}\right)^{n}=a^{m n}$[/tex]
An exponent refers to the number of times a number exists multiplied by itself.
For instance, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 exists not the exact as 2 x 3 = 6.
Given:
[tex]$8^{y}=16^{y+2}$[/tex]
To find:
the values of y.
3y = 4 (y + 2)
Simplifying the above equation, we get
3y = 4(y + 2)
y = -8
The value of y = -8.
Therefore, the correct answer is option a. –8.
To learn more about exponent rules
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