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\left(y^{2}\right)^{5}\times \frac{1}{y^{10}}
Use the rules of exponents to simplify the expression.
y^{2\times 5}y^{10\left(-1\right)}
To raise a power to another power, multiply the exponents.
y^{10}y^{10\left(-1\right)}
Multiply 2 times 5.
y^{10}y^{-10}
Multiply 10 times -1.
y^{10-10}
To multiply powers of the same base, add their exponents.
y^{0}
Add the exponents 10 and -10.
1
For any term t except 0, t^{0}=1.