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What is the value of y in the product of powers below?

What is the value of y in the product of powers below?-example-1

1 Answer

12 votes

Answer:

The value of y = 0

Explanation:

Given the equation


8^3\cdot 8^(-5)\cdot 8^(\:y)=8^(-2)

Apply exponent rule:
a^b\cdot \:a^c=a^(b+c)

so


8^3\cdot \:\:8^(-5)=8^(3-5)=8^(-2)=(1)/(8^2)=(1)/(64)

Thus, the equation becomes


(1)/(64)\left(8\:^y\right)=(1)/(64)

Divide both sides by 1/64


((1)/(64)\left(8\:^y\right))/((1)/(64))=((1)/(64))/((1)/(64))


8\:^y=1

Solve Exponent


8\:^y=1

Take log of both sides


\:log\left(8\:^y\right)\:=log\:\left(1\right)


y\cdot \left(log\left(8\right)\right)=log\left(1\right)


y\:=(log\left(1\right))/(\left(log\left(8\right)\right))


y = 0

Therefore, the value of y = 0

User RafaelTSCS
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