Math  /  Algebra

Question5. (2x2y)5\left(2 x^{2} y\right)^{5}

Studdy Solution

STEP 1

Assumptions
1. The expression to simplify is (2x2y)5(2x^2 y)^5.
2. We need to apply the power rule for exponents.

STEP 2

Recall the power rule for exponents, which states that (am)n=amn(a^m)^n = a^{m \cdot n}.

STEP 3

Apply the power rule to each component inside the parentheses. The expression (2x2y)5(2x^2 y)^5 can be broken down into three parts: 22, x2x^2, and yy.

STEP 4

First, apply the power rule to the constant 22:
(2)5=25(2)^5 = 2^5

STEP 5

Next, apply the power rule to x2x^2:
(x2)5=x25=x10(x^2)^5 = x^{2 \cdot 5} = x^{10}

STEP 6

Finally, apply the power rule to yy:
(y)5=y5(y)^5 = y^5

STEP 7

Combine all the results from the previous steps to get the simplified expression:
25x10y52^5 \cdot x^{10} \cdot y^5

STEP 8

Calculate 252^5:
25=322^5 = 32

STEP 9

Substitute 3232 back into the expression:
32x10y532 \cdot x^{10} \cdot y^5
The simplified expression is 32x10y532x^{10}y^5.

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