Math

QuestionSimplify the expression: (2y6)3(2 y^{6})^{3}.

Studdy Solution

STEP 1

Assumptions1. We are given the expression (y6)3\left( y^{6}\right)^{3}. . We need to simplify this expression.

STEP 2

We can simplify this expression by applying the power of a power rule. The power of a power rule states that (am)n=amn(a^{m})^{n} = a^{m \cdot n}.
(2y6)=2(y6)\left(2 y^{6}\right)^{} =2^{} \cdot \left(y^{6}\right)^{}

STEP 3

Now, calculate the power of2.
23=82^{3} =8So, the expression becomes8(y6)38 \cdot \left(y^{6}\right)^{3}

STEP 4

Next, apply the power of a power rule to the term (y6)3\left(y^{6}\right)^{3}.
(y6)3=y63\left(y^{6}\right)^{3} = y^{6 \cdot3}

STEP 5

Calculate the power of y.
y3=y18y^{ \cdot3} = y^{18}So, the expression becomes8y188 \cdot y^{18}

STEP 6

Finally, write the simplified expression.
8y188y^{18}So, (2y6)3\left(2 y^{6}\right)^{3} simplifies to 8y188y^{18}.

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