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the answer to this equation is negative 6 but I don’t know to explain how I got the answer is word form.

the answer to this equation is negative 6 but I don’t know to explain how I got the-example-1

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The value of k is –6.

Solution:

Given equation:


$(5 \cdot 5^(k))/(5^(-8))=5^(3)

To find the value of k:


$(5 \cdot 5^(k))/(5^(-8))=5^(3)

Using exponent rule:
a^m \cdot a^n = a^(m+n)


$(5^(1+k))/(5^(-8))=5^(3)

Using exponent rule:
(1)/(a^(-m)) = a^(m)


$ 5^(1+k) \cdot 5^(8)=5^(3)

Using exponent rule:
a^m \cdot a^n = a^(m+n)


$ 5^(1+k+8)=5^(3)


$ 5^(k+9)=5^(3)

If the bases are same then, we can equate the powers of the bases.

i. e. If
a^m = a^n then m = n.

k + 9 = 3

Subtract 9 from both sides of the equation, we get

k = –6

Hence the value of k is –6.

User Sumit Kapoor
by
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