Question

Find all expressions below that are equivalent to (3)^4(10)^4

Answer 1

Answer:

1, and 3 are equivelent to (3)^4(10)^4

Step-by-step explanation:

(3)^4(10)^4 = 810000

1. (3^2)^2 * (10^2)^2

   (9)^2   *   (100)^2

      81     *   10000

     810000

2. (13)^4 = 28561

3. (3 * 10)^4

      (30)^4

       810000

Answer 2

The second expression $(3^2)^2(10^2)^2$ and the fourth expression $(3$ × $10)^4$ are equivalent to the first expression $(3)^4(10)^4$.

Given the following mathematical expression;

$(3)^4(10)^4$  .....expression 1.

• In this exercise, you're required to find which of the mathematical expressions are equivalent to the above expression.

Second expression:

$(3^2)^2(10^2)^2$

We would simplify exp. 1 to determine whether or not it is equal to exp. 2;

The powers of exp. 1 are both 4. Also, 2 is a common factor of 4.

$4 = 2$ × $2$

Therefore, we would replace the value of 4 with its common factors (2);

$(3)^4(10)^4 = (3)^2^*^2$ × $(10)^2^*^2$

$(3)^4(10)^4 = (3^2)^*^2$ × $(10^2)^*^2$

$(3)^4(10)^4 = (3^2)^2$ × $(10^2)^2$

Simplifying further, we have;

$81$ × $10000$ $= (9)^2$ × $(100)^2$

$81$ × $10000$ $= 81$ ×

$810,000 = 810,000$ (It is equivalent)

Third expression:

$(13)^{4}$

By mere inspection, we can tell that the above expression isn't equal to exp. 1 because the arithmetic operation between its values is multiplication but not addition.

$(3)^4(10)^4 \neq (13)^{4}$

Simplifying further, we have;

$81$ × $10000$ $\neq (13)^4$

$81$ × $10000$ $\neq$ $13$ ×

$810,000 \neq 28,561$ (It is not equivalent)

Fourth expression:

$(3$ × $10)^4$

According to the law of indices, when the powers of two numbers are the same we would multiply the numbers together and maintain their power.

$(3)^4(10)^4 =$ $(3$ × $10)^4$

Simplifying further, we have;

$81$ × $10000$ $= 30^4$

$81$ × $10000 =$  $30$ ×

$810,000$ $= 810,000$ (It is equivalent)

In conclusion, the second expression and the fourth expression are equivalent to the first expression.

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