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2 years ago

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

Mathematics

2 answers:

Marat540 [252]2 years ago

8 0

Answer:

y =0

Step-by-step explanation:

From the equation;

8³ × 8⁻⁵×8^y = 8⁻²= 1/8²

From the laws of indices;

aⁿ×aⁿ = a^2n

Therefore;

8³ × 8⁻⁵×8^y = 8^(3+-5+y)

8^(-2+y) = 8^-2 ; but the bases are the same and thus the exponents are the same;

-2 + y = -2

y = 0

makkiz [27]2 years ago

6 0

Answer:

The value of y is 0

Step-by-step explanation:

8³ * 8^-5*8^y = 8^-2 or 1/8²

Taking indices of both sides

From first law of indices;

Multiplication sign change to addition; i.e. x^a * x^b = x^(a + b).

So,

8³ * 8^-5*8^y = 8^-2

Becomes

8^(3 + (-5) + y) = 8^-2

Same base of 8 can cancel one another. So, we're left with

3 + (-5) + y = -2

Open the bracket

3 - 5 + y = -2

-2 + y = -2

Make y the subject of formula

y = 2 - 2

y = 0

Hence, the value of y in the equation is 0

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