Question

find the value of xpower 12/7 -x power 5/7​

Answer 1

Answer:

The  value of  $x^{\frac{12}{7} }$ - $x^{\frac{5}{7} }$ is   $x^{\frac{5}{7}}(x - 1)$

Step-by-step explanation:

To find,

The value of $x^{\frac{12}{7} }$ - $x^{\frac{5}{7} }$

Recall the formula

xᵃ⁺ᵇ = xᵃ×xᵇ

Solution:

$x^{\frac{12}{7} }$ - $x^{\frac{5}{7} }$ = $x^{\frac{5+7}{7}} - x^{\frac{5}{7}$

= $x^{\frac{5}{7}+\frac{7}{7} } - x^{\frac{5}{7}$

By applying the identity xᵃ⁺ᵇ = xᵃ×xᵇ we get

= $x^{\frac{5}{7}}(x^\frac{7}{7} } - 1)$

= $x^{\frac{5}{7}}(x - 1)$

$x^{\frac{12}{7} }$ - $x^{\frac{5}{7} }$ = $x^{\frac{5}{7}}(x - 1)$

∴ The  value of  $x^{\frac{12}{7} }$ - $x^{\frac{5}{7} }$ is  $x^{\frac{5}{7}}(x - 1)$

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Answer 2

Question: Find the value of $x^{\frac{12}{7} }-x^{\frac{5}{7} }$.

Answer:

The value of the given expression is $x=0$ and $x=1$.

Step-by-step explanation:

Some rules of exponents are:-

• $a^ma^n=a^{m+n}$
• $(a^m)^n=a^{mn}$
• $\frac{a^m}{a^n}=a^{m-n}$

Step 1 of 1

To find the value of the expression $x^{\frac{12}{7} }-x^{\frac{5}{7} }$.

Consider the given expression as follows:

$x^{\frac{12}{7} }-x^{\frac{5}{7} }$

Rewrite the expression as follows:

⇒ $x^{\frac{5}{7} +\frac{7}{7} }-x^{\frac{5}{7} }$

Using the rule of exponent, $a^ma^n=a^{m+n}$

⇒ $x^{\frac{5}{7} }x^{\frac{7}{7} }-x^{\frac{5}{7} }$

⇒ $x^{\frac{5}{7} }x-x^{\frac{5}{7} }$

Take the term $x^{\frac{5}{7} }$ common out as follows:

⇒ $x^{\frac{5}{7} }(x-1)$

Now, the equate the expression equal to zero as follows:

⇒ $x^{\frac{5}{7} }(x-1)=0$

⇒ $x^{\frac{5}{7} }=0$ and $x-1=0$

1) For $x^{\frac{5}{7} }=0$,

The value of $x$ is,

$x=0$

2) For $x-1=0$,

The value of $x$ is,

$x=1$

Final answer: The value of the given expression is $x=0$ and $x=1$.

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