Use the properties of exponents to determine the value of aa for the equation:left bracket, x, start superscript, one fifth, end superscript, right bracket, cubed, start root, start index, 5, end index, x, to the power 4 , end root, equals, x, to the power a(x 51 ) 3 5 x 4 =x a
Question
Use the properties of exponents to determine the value of aa for the equation:left bracket, x, start superscript, one fifth, end superscript, right bracket, cubed, start root, start index, 5, end index, x, to the power 4 , end root, equals, x, to the power a(x 51 ) 3 5 x 4 =x a
Solution
The equation you provided is a bit unclear, but I'll assume you're asking about the following equation:
(x^(1/5))^3 * (5√(x^4)) = x^a
Let's solve it step by step:
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Simplify the left side of the equation:
(x^(1/5))^3 * (5√(x^4)) = x^(3/5) * x^(4/5)
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Use the property of exponents that says x^m * x^n = x^(m+n) to combine the two terms:
x^(3/5) * x^(4/5) = x^(3/5 + 4/5) = x^1
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So, the left side of the equation simplifies to x.
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Therefore, the equation x = x^a implies that a = 1.
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