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QOTD#24 If , then what is the value of x?
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30 Apr 2017, 13:56
30 Apr 2017, 13:56
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Question Stats:
97% (00:38) correct
2% (04:31) wrong based on 34 sessions
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If \(\frac{(x^{1.5})^{2}}{x^{6}}= 8^{-1}\), then what is the value of x?
Drill 4
Question: 8
Page: 322
Question: 8
Page: 322
Show: :: OA
2
Re: QOTD#24 If , then what is the value of x?
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04 May 2017, 01:09
04 May 2017, 01:09
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Explanation
To solve this question, remember the rules of exponents. When an exponent is outside a parentheses, it gets multiplied to any exponents inside the parentheses; thus \((x^{1.5})^2 = x^3\).
Next, since when two numbers of the same base are divided, the exponents are subtracted, \(x^3\) divided by \(x^6\) is \(\frac{x^3}{x^6}= x^{3-6}= x^{-3}\).
Since a negative exponent is equal to its reciprocal, then \(x^{-3}= \frac{1}{x^3} = 8^{-1}= \frac{1}{8}=\frac{1}{2^3}\).
Thus \(x^3=2^3\).
Hence x=2.
To solve this question, remember the rules of exponents. When an exponent is outside a parentheses, it gets multiplied to any exponents inside the parentheses; thus \((x^{1.5})^2 = x^3\).
Next, since when two numbers of the same base are divided, the exponents are subtracted, \(x^3\) divided by \(x^6\) is \(\frac{x^3}{x^6}= x^{3-6}= x^{-3}\).
Since a negative exponent is equal to its reciprocal, then \(x^{-3}= \frac{1}{x^3} = 8^{-1}= \frac{1}{8}=\frac{1}{2^3}\).
Thus \(x^3=2^3\).
Hence x=2.
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Re: QOTD#24 If , then what is the value of x?
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26 Apr 2020, 13:11
26 Apr 2020, 13:11
sandy wrote:
If \(\frac{(x^{1.5})^{2}}{x^{6}}= 8^{-1}\), then what is the value of x?
Drill 4
Question: 8
Page: 322
Question: 8
Page: 322
Show: :: OA
2
Given: \(\frac{(x^{1.5})^{2}}{x^{6}}= 8^{-1}\)
Apply the Power of a Power law to simplify the numerator: \(\frac{x^3}{x^{6}}= 8^{-1}\)
Apply the Quotient law to simplify the left side: \(x^{-3}= 8^{-1}\)
Rewrite \(8\) as a power of \(2\) to get: \(x^{-3}= (2^3)^{-1}\)
Apply the Power of a Power law to simplify the right side \(x^{-3}= 2^{-3}\)
At this point we can see that \(x=2\)
Answer: \(2\)
Cheers,
Brent
