Respuesta :
The value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
How to simplify power raised by another number?
When the power of a number is raised by another number, then multiply both the powers and the result of this product keep as the power of the number.
Let suppose there is a number a. For this number the above rule can be given as,
[tex](a^m)^n=a^{m\times n}\\(a^m)^n=a^{mn}[/tex]
The expression which consist unknown variable y is given as,
[tex]8^y=16^{y+2}[/tex]
The above equation can be written as,
[tex](2\times2\times2)^y=(2\times2\times2\times2)^{y+2}\\(2^3)^y=(2^4)^{y+2}\\(2)^{3y}=(2^)^{4y+8}[/tex]
As the base of both side of the equation is same. Thus, the value of their exponent can be compared.
[tex]3y=4y+8\\4y-3y=-8\\y=-8[/tex]
Thus, the value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
Learn more about the power raised by another number here;
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