Question

express (216)^(-2) as a power with base 6

Answer 1

Hi friend,

Here is your answer,
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(216)⁻² 

=> (6³)⁻²

=> (6)⁻⁶
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Answer 2

Answer:

Required answer is ${6}^{( - 6)}$

Step-by-step explanation:

Given,

${216}^{ (- 2)}$

Here we want to express given term as a power with base 6.

By prime factorisation,

$216 = 6 \times 6 \times 6 \\ = {6}^{3}$

So,

${216}^{( - 2)} \\ = { {6}^{3} }^{ ( - 2)} \\ = {6}^{(3 \times ( - 2))} \\ = {6}^{ - 6}$

Here applied formula is

${x}^{ {a}^{b} } = {x}^{a \times b}$

This is a problem of Power of indices.

Some more 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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