Question

Which expressions below are equivalent to (3)^4 (10)^4

Answer 1

810000

Explanation:

900^2

(3^2)^2.(10^2)^2

(3.10)^4

Answer 2

From the given options, options A, C, and G are equivalent to
`$(3)^4(10)^4$`

The expression
`$(3)^4(10)^4$` means raising 3 to the power of 4 and multiplying it by 10 raised to the power of 4. Let's simplify each option to see which ones are equivalent to this expression.

A.
`$\left[(3 \cdot 10)^4\right]^4$`:

Simplifying the expression inside the brackets first, we have
`$(3 \cdot 10)^4 = 30^4$`. Then, raising
`$30^4$` to the power of 4 gives us
`$(30^4)^4 = 30^(16)$`. This is equivalent to the original expression.

B.
`$900^2$`:

Simplifying
`$900^2$` gives us
`$900 \cdot 900 = 810,000$`. This is not equivalent to the original expression.

C.
`$30^(16)$`:

This is the same expression we obtained in option A. Therefore, it is equivalent to the original expression.

D.
`$(30)^8$`:

Raising 30 to the power of 8 gives us
`$30 \cdot 30 \cdot 30 \cdot 30 \cdot 30 \cdot 30 \cdot 30 \cdot 30$`. This is not equivalent to the original expression.

E.
`$\left(3^2\right)^2 \cdot \left(10^2\right)^2$`:

Simplifying
`$3^2$` gives us 9, and simplifying
`$10^2$` gives us 100. Then,
`$(9)^2 \cdot (100)^2 = 81 \cdot 10,000$`. This is not equivalent to the original expression.

F.
`$(13)^4$`:

This is a different expression and not equivalent to the original expression.

G.
`$(3 \cdot 10)^4$`:

Simplifying
`$3 \cdot 10$` gives us 30. Then, raising 30 to the power of 4 gives us
`$30^4$`. This is equivalent to the original expression.