Question

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

Answer 1

The value of k is –6.

Solution:

Given equation:

$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}$

To find the value of k:

$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}$

Using exponent rule: $a^m \cdot a^n = a^{m+n}$

$\frac{5^{1+k}}{5^{-8}}=5^{3}$

Using exponent rule: $\frac{1}{a^{-m}} = a^{m}$

$5^{1+k} \cdot 5^{8}=5^{3}$

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.