Question

if (-5/7)^-4×(-5/7)^12={(-5/7)^3}^x ×(-5/7)-1 find the value of x .anyone who will answer my question I will be marking it brainliest
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Answer 1

we have

(-5/7)^-4 × (-5/7)^12={(-5/7)^3}^x ×(-5/7)^-1

we know that when base are equal then power will also equal

therefore -4+12=3x+(-1)
=》8=3x-1
=》8+1=3x
=》9=3x
=》9/3=x
=》3=x
hence the x=3

Answer 2

Answer:

Required value of x is 3.

Step-by-step explanation:

Given,

${( - \frac{5}{7} )}^{ - 4} \times {( - \frac{5}{7} )}^{12} = {( - \frac{5}{7} )}^{ 3^{ x} } \times {( - \frac{5}{7} )}^{ - 1} \\ {( - \frac{5}{7} )}^{ - 4 + 12} = {( - \frac{5}{7} )}^{ 3x} \times {( - \frac{5}{7} )}^{ - 1} \\ {( - \frac{5}{7} )}^{ 8} = {( - \frac{5}{7} )}^{ 3x - 1} \\ 8 = 3x - 1 \\ 3x = 8 + 1 \\ 3x = 9 \\ x = \frac{9}{3} \\ x = 3$

Required value of x is 3

Here applied formula is

${x}^{ \frac{y}{z} } = {x}^{yz} \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ if \: {x}^{a} = {x}^{b} \: then \: a = b$

This is a problem of Power of indices .

Some important formulas of Power of indices :

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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