Question

Simplify the following 4^4×(5/4)^4

Answer 1

Answer:

....................

Answer 2

Answer:

Required answer is 625.

Step-by-step explanation:

Given,

${4}^{4} \times {( \frac{5}{4} )}^{4}$

We know,

${ (\frac{x}{y}) }^{d} = \frac{ {x}^{d} }{ {y}^{d} }$

So,

${ (\frac{5}{4} )}^{4} \\ = \frac{ {5}^{4} }{ {4}^{4} }$

Now,

${5}^{4} \\ = 5 \times 5 \times 5 \times 5 \\ = 625$

and

${4}^{4} \\ = 4 \times 4 \times 4 \times 4 \\ = 216$

So,

$\frac{ {5}^{4} }{ {4}^{4} } \\ = \frac{625}{216}$

So,

${4}^{4} \times {( \frac{5}{4} )}^{4} \\ = 216 \times \frac{625}{216} \\ = 625$

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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