Question

Please help me someone

Answer 1

To solve this, you need to know three exponent rules:
1) Power of a product
Basically says $(ab)^{2} = a^{2} b^{2}$. This means a product raised to a power is the same as taking each factor to that power and multiplying them.

For example: $(5a)^{2} = 5^{2} a^{2}$

2) Product of powers
Basically says $a^{m} a^{n} = a^{m+n}$. When two expressions with the same base (a) are multiplied, you can add their exponents while keeping the same base.

For example: $a^{2} a^{3} = a^{2+3} = a^{5}$

3) Power of a power
Basically says $(a^{m})^{n} = a^{m \times n}$. When an exponent is being raised to a exponent, you can multiply the exponents.

For example: $(a^{2})^{3} = a^{(2 \times 3)} = a^{6}$
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Back to your problem:
You are asked to simplify $(6x^{2} y)^{2} (y^{2})^{3}$, Tackle it by simplifying both factors and then multiplying them together and simplifying again.

1) First use the power of a product rule to change $(6x^{2} y)^{2}$ into $6^{2} (x^{2})^{2} y^{2}$. Simplify it into $36 x^{4} y^{2}$ using the power of a power rule.

2) Simplify $(y^{2})^{3}$ into $y^{6}$ using the power of a power rule.

3) Multiply the simplified factors from part one and two and simplify using the product of powers rule:
$(36 x^{4} y^{2})(y^{6})\\ = (36 x^{4})(y^{2} y^{6})\\ = (36 x^{4})(y^{2+6}) \\ = 36 x^{4}y^{8}$

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Answer: $36 x^{4}y^{8}$