Question

If 5^6×1/5^x= 1/5^10, then what is x​

Answer 1

Answer:

X=16

Step-by-step explanation:

1. 5^ 6 x 1 by 5 x is equals to 1 by 5 ^ 10
2. 5 to the power of minus x + 6 is equals to 1 by 5 ^ 10

• as the basis of both are same 5 and 5 so they both submit and get same and therefore the exponent of those both will carries by only one and into one is equals to five because any number multiplied by 1 is equals to itself

1. in the left hand side one by five to the power of 10 if it reciprocal that it would become 5 to the power of minus 10 when we reciprocal that the symbol of the exponent changes to negative
2. when the basis of lhs and RHS are same they got submerged together as he did in the first step so like that we could cancel both the five
3. so it becomes -X+6 is equals to minus 10

X is 16

Answer 2

Answer:

$given \: that \\ {5}^{6} \times \frac{1}{ {5}^{x} } = \frac{1}{ \frac{5}{10} } \\ \ {5}^{6} \times \frac{1}{ {5}^{x} } = {5}^{ - 10} \\ \frac{1}{ {5}^{x} } = {5}^{ - 10} \div {5}^{6}$

${5}^{ - x} = {5}^{ - 10 - 6} \\ {5}^{ - x} = {5}^{ - 16} \\ - x = - 16$

$x = 16 \: ans...$

Step-by-step explanation:

I hope it will help...