(Y^3)^7•(y^7)^5

Answer 1

To simplify the expression \((Y^3)^7 \cdot (y^7)^5\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Applying that property, we have:

1. \((Y^3)^7 = Y^{3 \cdot 7} = Y^{21}\)
2. \((y^7)^5 = y^{7 \cdot 5} = y^{35}\)

Now we can combine the two results:

\[ Y^{21} \cdot y^{35} \]

Since \(Y\) and \(y\) are different variables, we cannot combine them further. Thus, the final simplified expression is:

\[ Y^{21}y^{35} \]

Answer 2

I think it's clear that the capital Y is supposed to be the same as the lower-case y. So the answer is y^56

Answer 3

Thank you for the clarification! If we assume that the capital \(Y\) is indeed the same as the lowercase \(y\), then we can simplify the expression as follows:

Starting with the original expression:

\[ (Y^3)^7 \cdot (y^7)^5 \]

If \(Y = y\), we can rewrite it as:

\[ (y^3)^7 \cdot (y^7)^5 \]

Now, applying the power of a power property:

1. \((y^3)^7 = y^{3 \cdot 7} = y^{21}\)
2. \((y^7)^5 = y^{7 \cdot 5} = y^{35}\)

Now, we combine these:

\[ y^{21} \cdot y^{35} = y^{21 + 35} = y^{56} \]

So, the final answer is:

\[ y^{56} \]

Thank you for pointing that out!