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Please help me with this math question (exponents )

please show how you solved it thank you in advance <3

Please help me with this math question (exponents ) please show how you solved it-example-1
User Jason Lin
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1 Answer

4 votes


√(4) 3^(17)The simplified expressions are:


\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}} = 2


\sqrt[4]{3^(17) + 9^(6)} = 3^(11/2)

To solve the radicals in the image, we can use the following properties of exponents:


\sqrt[n]{a^(m) } =
a^{(m)/(n) }


a^(b) .
a^(c) =
a^(b+c)

For the first radical, we can use the first property to simplify it as follows:


\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}}=
\sqrt[3]{2^2 \cdot 2^(1/4)} =
\sqrt[3]{2^3} =
\boxed{2}

For the second radical, we can use the second property to simplify it as follows:


\sqrt[4]{3^(17) + 9^(6)} = +
(3^2)^6} =
√(4) 3^(17) + 3^{12}} =
√(4){3^(17)
\cdot
(1 + 3^(5))}

We can then use the first property to simplify the square root as follows:


\sqrt{43^(17) } .
(1 + 3^(5))} =
\sqrt{43^(17) } . 243} =
√(4) 3^(17) .
3^5 =
\sqrt[4]{3^(22)} =
\boxed{3^(11/2)}

Therefore, the simplified expressions are:


\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}} = 2


\sqrt[4]{3^(17) + 9^(6)} =
3^(11/2)

User Curtybear
by
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