Question

If x and y are positive real numbers, which expression is equivalent to the expression below: (49x^2)|(27y^0)?

A. 10.03y
B. 10x^2y
C. 21337
D. 21.1972

Answer 1

B.
`10x^2y`

Step-by-step explanation:

The expression
`(49x^2)|(27y^0)`simplifies as follows:

`\[ (49x^2)|(27y^0) = (7x)^2 * 3^0 \]`

Any non-zero number raised to the power of zero is always 1, so
`\(3^0 = 1\).`Thus, the expression further simplifies to:

`\[ (7x)^2 * 1 = 49x^2 \]`

Now, the expression is reduced to
`\(49x^2\).`To find an equivalent expression, we observe that
`\(49x^2\)`is the same as
`\(7^2 * x^2\),`which can be factored as
`\((7x)^2\).`

Therefore, the equivalent expression is \(10 \times
`(7x)^2 * y\)`, and this can be further simplified to
`\(10x^2y\).`

In conclusion, the final equivalent expression is
`\(10x^2y\)`, which corresponds to option B. The key steps in the simplification involve recognizing the power of zero rule and factoring
`\(49x^2\).`