# Calculate: sqrt(150x^{16)y^9}

## Expression: $\sqrt{ 150{x}^{16}{y}^{9} }$

Write the expression as a product where the root of one of the factors can be evaluated

$\sqrt{ 25 \times 6{x}^{16}{y}^{9} }$

Rewrite the exponent as a sum where one of the addends is a multiple of the index

$\sqrt{ 25 \times 6{x}^{16}{y}^{8+1} }$

Write the expression in exponential form with the base of $5$

$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8+1} }$

Use ${a}^{m+n}={a}^{m} \times {a}^{n}$ to expand the expression

$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8} \times {y}^{1} }$

Any expression raised to the power of $1$ equals itself

$\sqrt{ {5}^{2} \times 6{x}^{16}{y}^{8} \times y }$

The root of a product is equal to the product of the roots of each factor

$\sqrt{ {5}^{2} }\sqrt{ {x}^{16} }\sqrt{ {y}^{8} }\sqrt{ 6y }$

Reduce the index of the radical and exponent with $2$

$5\sqrt{ {x}^{16} }\sqrt{ {y}^{8} }\sqrt{ 6y }$

Reduce the index of the radical and exponent with $2$

$5{x}^{8}\sqrt{ {y}^{8} }\sqrt{ 6y }$

Reduce the index of the radical and exponent with $2$

$5{x}^{8}{y}^{4}\sqrt{ 6y }$

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