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3 years ago

Can anyone help me with this?

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

3 0

Answer: 16y² - x²

Step-by-step explanation: The - sign means a difference, so the choices with + signs are eliminated (though 64x² and 9 are squares)

10 is not a square so that one is eliminated (though the y² and the 4x² are squares)

16 is the square of 4, y² is the square of y, and x² is the square. That expression shows a difference of squares.

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Answer:

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Step-by-step explanation:

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kiruha [24]

For this case we have the following expression:

$\frac {216 ^ {n-2}} {(\frac {1} {36}) ^ {3n}} = 216$

We multiply both sides by: $(\frac {1} {36}) ^ {3n}$

$216 ^ {n-2} = 216 * (\frac {1} {36}) ^ {3n}$

We divide both sides by 216:

$\frac {216 ^ {n-2}} {216} = (\frac {1} {36}) ^ {3n}$

To divide powers of the same base, we place the same base and subtract the exponents:

$216 ^ {n-2-1} = (\frac {1} {36}) ^ {3n}\\216 ^ {n-3} = (\frac {1} {36}) ^ {3n}$

Rewriting:

$(6 ^ 3) ^ {n-3} = (\frac {1} {6 ^ 2}) ^ {3n}\\6 ^ {3n-9} = \frac {1} {6 ^ {6n}}\\6^{ 3n-9} * 6^{ 6n} = 1$

To multiply powers of the same base, we place the same base and add the exponents:

$6^{ 3n-9 + 6n} = 1\\6^{ 9n-9} = 1$

We know that any number raised to zero is 1, $a ^ 0 = 1.$

So, for equality to be true:

$9n-9 = 0\\9n = 9\\n = \frac {9} {9}\\n = 1$

Answer:

$n = 1$

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