Rewrite the expression as an equivalent radical expression.
y^(1/6)
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Hint: To add the nth root symbol (√), type “root”
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Simplify the following expression.
(x^(10)b^(10))^5
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Hint: To add an exponent (x^y), type “exponent” or press “^”
x^(50)/b^(50)
x^(50)b^(50)
x^(150)b^(50)
Rationalize the denominator.
6/√11
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Hint: To add the square root symbol (√), type “root”
Sure! Let’s tackle each part of your question step by step.
1. Rewrite the expression as an equivalent radical expression:
The expression given is (y^{1/6}). To rewrite this as a radical expression, you want to express it using the nth root. The general form is:
[
y^{1/n} = sqrt[n]{y}
]
So, for (y^{1/6}):
[
y^{1/6} = sqrt[6]{y}
]
2. Simplify the following expression:
You have ((x^{10}b^{10})^5). To simplify this, apply the power of a product rule, which states that ((ab)^n = a^n b^n):
[
(x^{10}b^{10})^5 = x^{10 cdot 5} b^{10 cdot 5} = x^{50} b^{50}
]
3. Rationalize the denominator:
You need to rationalize the denominator of (frac{6}{sqrt{11}}). To do this, multiply the numerator and the denominator by (sqrt{11}):
[
frac{6}{sqrt{11}} cdot frac{sqrt{11}}{sqrt{11}} = frac