Question

5^3*5^x which expressions are equivalent to the one below? check all that apply. A). 5^3x B). 125*5^x C). 25^3x D). 5^3+x E). (5*x)^3 F). 5^3-x

Answer 1

The equivalent expressions are
`5^(3x)`,
`125 * 5^x`, and
`(5*x)^3.`

Step-by-step explanation:

The expression
`5^3 * 5^x` can be simplified using the rule of multiplying exponentiated quantities: when multiplying the same base with different exponents, we can add the exponents together. In this case, we have 5 raised to the power of 3 multiplied by 5 raised to the power of x. Therefore, the equivalent expressions are:

• A)
  `5^(3x)`
• B)
  `125 * 5^x`
• E)
  `(5*x)^3`

These expressions have combined the exponents by addition or multiplication, resulting in equivalent forms of the original expression.

Answer 2

Option D -
`5^3* 5^x=5^(3+x)`

Step-by-step explanation:

Given : Expression
`5^3* 5^x`

To find : Which expression is equivalent to given expression?

Solution :

The given expression is
`5^3* 5^x`

As we see the bases are same i.e. 5.

Applying property that if in multiplication bases are same then powers get added
`x^a* x^b=x^(a+b)`

`=5^3* 5^x`

`=5^(3+x)`

Therefore, Option D is correct.

The required equivalent form is
`5^3* 5^x=5^(3+x)`