Question

3^-7÷3^-4 use law of exponent​

Answer 1

Answer:

To Find:

Value of the expression after using the law of exponents in the expression:

$\tt{{3}^{ - 7} \div {3}^{ - 4} }$

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We know,

$\boxed{\sf\blue{{x}^{y} \div {x}^{x} = {x}^{y - x} }}$

We will use the same law here.

$\tt{{3}^{ - 7} \div {3}^{ - 4} }$

[Expression given in the question]

$\tt{= {3}^{(-7) - (-4)} }$

[Written as per the rule]

$\tt{ ={3}^{-7 + 4}}$

[We know that, (-) + (-) = (+)]

$\tt{={3}^{-3}}$

[Simplification of the integers]

$\tt{=\frac{1}{{3}^{3}}}$

[Removed the negative sign from the exponent]

$\tt{=\frac{1}{3 \times 3 \times 3}}$

[Expanded the denominator]

$\tt\green{=\frac{1}{27}}$

[SOLUTION]

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Required Answer:

After evaluation of $\bf{{3}^{ - 7} \div {3}^{ - 4} }$, we got $\boxed{\bf\green{=\frac{1}{27}}}$.

Answer 2

Answer:

Step-by-step explanation:

$[a^{m} * a^{n} = a^{m+n} ]$

$3^{-7} divided by 3^{-4}$

$3^{-7-(-4)}$

$= 3^{-7+4}$

= $3^{-3} = \frac{1}{27}$